CBSE Class 12

NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves

NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves are part of NCERT Solutions for Class 12 Physics. Here we have given. NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves

Question 1.
Figure shows a capacitor made of two circular plates each of radius 12 cm and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in figure). The charging current is constant and equal to 0.15 A.
(a) Calculate the capacitance and the rate of change of potential difference between the plates.
(b) Obtain the displacement current across the plates.
(c) Is Kirchhoffs first rule valid at each plate of the capacitor ? Explain.

Answer:

Yes. Because conduction current entering one plate is equal to the displacement current leaving that plate.

Question 2.
A parallel plate capacitor (shown in the figure) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V a.c. supply with an (angular) frequency of 300 rad s^_1.
(a) What is the r .m.s. value of the conduction current?
(b) Is the conduction current equal to the displacement current?
(c) Determine the amplitude of \( \overrightarrow { B } \) at a point 3.0 cm from the axis between the plates.

Answer:

Question 3.
What physical quantity is the same for X-rays of g g wavelength 10^-10 m, the red light of wavelength 6800 A, and radiowaves of wavelength 500 m?
Answer:
The speed in a vacuum is the same for all are c = 3 x 10⁸ ms^-1. (Electromagnetic waves)

Question 4.
A plane electromagnetic wave travels in a vacuum along Z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?
Answer:
The electric field vector \( \overrightarrow { E } \) and magnetic field vector\( \overrightarrow { B } \) are in xy plane. They are normal to each other.

Question 5.
A radio can tune into any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band ?
Answer:

=> The corresponding wavelength band is 40 m to 25 m.

Question 6.
A charged particle oscillates about its mean equilibrium position with a frequency of 10⁹ Hz. What is the frequency of the electromagnetic waves produced by the oscillator?
Answer:
The frequency of the electromagnetic waves produced is the same as that of the oscillating charged particle. Hence the frequency of the electro­magnetic waves produced is, υ= 10⁹ Hz.

Question 7.
The amplitude of the magnetic field part of a harmonic electromagnetic wave in a vacuum is B₀ =510 nT. What is the electromagnetic waves produced by the oscillator?
Answer:

Question 8.
Suppose that the electric field amplitude of an electromagnetic wave is E₀ = 120 N/C and that its frequency is v = 50.0 MHz.
(a) Determine, B₀, ω, k and λ.
(b) Find expressions for E and B.
Answer:

Question 9.
The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = hv (for the energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?
Answer:
Using the relation for photon energy,


Conclusion. The above result indicates that the different wavelengths in the electromagnetic spectrum can be obtained by multiplying roughly the powers often.
The visible wavelengths are spaced by a few eV.
The nuclear energy levels (from y rays) are spaced about 1 MeV.

Question 10.
In-plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 x 10¹⁰ Hz and amplitude 48 Vm^_1.
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density of the B field. [c= 3 x 10⁸ ms^-1].
Answer:

Question 11.
Suppose that the electric field part of an electromagnetic wave in a vacuum is
E = {(3.1 N/C) cos[(1.8 rad/m)y + (5.4 x 10⁶ rad/s)f]}\(\hat { i } \).
(a) What is the direction of propagation?
(b) What is the wavelength X?
(c) What is the frequency v?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave.
Answer:

Question 12.
About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation?
(a) at a distance of 1 m from the bulb?
(b) at a distance of 10 m?
Assume that the radiation is emitted isotropically and neglect reflection.
Answer:

Question 13.
Use the formula λ_mT = 029 cm K to obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?
Answer:

These numbers tell us the range of temperature required to obtain the different parts of the spectrum. For example, to obtain a wavelength of 1 μm, a temperature of 2900 K is required.

Question 14.
Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.
(a) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).
(b) 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift.)
(c) 2.7 K (temperature associated with the isotropic radiation filling all space-thought to be a relic of the ‘big-bang’ origin of the universe.)
(d) 5890 Å-5896 Å (double lines of sodium)
(e) 14.4 keV [energy of a particular transition in ⁵⁷Fe nucleus associated with a famous high-resolution spectroscopic method (Mossbauer spectroscopy).]
Answer:
(a) Radio waves (short-wavelength end)
(b) Radio waves (short-wavelength end)
(c)

(d) Given wavelength is of the order of 10^-7 m i.e visible radiations(yellow light)

Question 15.
Answer the following questions:

1. Long-distance radio broadcasts use shortwave bands. Why?  (C.B.S.E. 2005)
   
2. It is necessary to use satellites for long-distance TV transmission. Why? (C.B.S.E. 2005)
   
3. Optical and radio telescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why? (C.B.S.E. 2009)
   
4. The small ozone layer on top of the stratosphere is crucial for human survival. Why ?(C.B.S.E. 2005, 2009)
   
5. If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?
6. Some scientists have predicted that a global nuclear war on the earth would be followed by a severe nuclear winter’ with a devastating effect on life on earth. What might be the basis of this prediction? (C.B.S.E. 1995)
   

Answer:

1. The ionosphere reflects waves in these bands.
2. Television signals are of >30 MHz penetrate the ionosphere. Therefore, reflection is effected by satellites.
3. The atmosphere absorbs X-rays. while visible and radio waves can penetrate it.
4. It absorbs ultraviolet radiation from the sun and prevents it from reaching the earth’s surface and causing damage to life.
5. The temperature of the earth would be lower because the Greenhouse effect of the atmosphere would be absent.
6. The clouds produced by global nuclear war would perhaps cover substantial parts of the sky preventing solar light from reaching many parts of the globe. This would cause a ‘winter’. against which life on earth cannot withstand.

We hope the NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves, help you. If you have any query regarding NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves, drop a comment below and we will get back to you at the earliest.

Here we are providing NCERT Solutions for Class 12 English Flamingo Poem 5 A Roadside Stand. Students can get Class 12 English A Roadside Stand NCERT Solutions, Questions and Answers designed by subject expert teachers.

A Roadside Stand NCERT Solutions for Class 12 English Flamingo Poem 5

A Roadside Stand NCERT Text Book Questions and Answers

A Roadside Stand Think it out 

Question 1.
The city folk who drove through the countryside hardly paid any heed to the roadside stand or to the people who ran it. If at all they did, it was to complain. Which lines bring this out? What was their complaint about?
Answer:
The lines that bring out the irritation of the passers-by are:
Or if ever aside a moment, the out of sorts
At having the landscape marred….
They complained that the disfigured paint of the stall spoilt the beauty of the landscape, the signposts pointed the wrong way and the stalls were not maintained.

Question 2.
What was the plea of the folk who had put up the roadside stand?
Answer:
The people of the roadside stand sat in prayer that some city traffic should stop by and buy their wares so that they could make some money to improve their life beyond mere survival.

Question 3.
The government and other social service agencies appear to help the poor rural people, but actually do them no good. Pick out the words and phrases the poet uses to show their double standards.
Answer:
The poet uses the word ‘greedy good-doers, beneficent beasts of prey’ and ‘enforcing benefits that are calculated’.

Question 4.
What is the ‘childish longing’ that the poet refers to? Why is it in vain?
Answer:
The poet refers to the tireless longing of the stall owners for some car to stop by and give them an opportunity to make some money. But they wait in vain because the cars just pass by without thinking of the hope and longing of the sad faces peeping from the windows. If at all they stop, it is to ask the way or to take turn.

Question 5.
Which lines tell us about the insufferable pain that the poet feels at the thought of the plight of the rural people?
Answer:
The lines that express the poet’s insufferable pain are:
I wonder how I should like you to come to me
And offer to put me gently out of my pain.

A Roadside Stand Extra Questions and Answers

A Roadside Stand Short Answer Questions

Question 1.
What is the untold sorrow of the owners of the roadside stand?
Answer:
The untold sorrow of the roadside stand owners is that nobody pays attention to the efforts of the country folk to make some money. The city folk just pass by their stalls without helping them to maike some money. Their lives have not progressed at all as they merely earn to survive.

Question 2.
What is the poet’s complaint in the poem?
Answer:
The poet does not complain like passers-by that the landscape has been marred. He is complaining about the lack of opportunity and encouragement to these people in the countryside. He is upset about the sorrow of those who had set up the roadside stall in the hope that people would stop by and some money would tickle into their palms.

Question 3.
Why do country people ask for money?
Answer:
The country people ask for money to improve their lives. They set up stalls on (he roadside in the hope that they would make some money by selling goods of daily use and make their life better, as they had seen in movies and as had been promised by the party in power.

Question 4.
What was the news that was doing the rounds?
Answer:
There was news that the people in power were planning to move all these rural people to the city next to the theatre and the big stores. Their lives would be secured and they would not have to worry about themselves any longer. They were promised that they would soon be pulled out of their poverty.

Question 5.
How would the innocent be soothed out of their wits?
Answer:
The selfish good-doers would outwit the simple innocent people into believing that their intentions and efforts were for their improvement, while they would be seeking their own profits from the labour of these folks.

Question 6.
Why are the cars called ‘selfish’?
Answer:
The poet has used a transferred epithet here. He actually means to call the car owners selfish as they just pass by without a thought for the plight of the owners of the roadside stands and if at all they do stop, it is either to complain or to turn their car round.

Question 7.
What is the sadness that lurks near the open window there?
Answer:
The poet is referring to the disappointed faces that wait in vain at their stall windows for someone to ask for their wares and drop some money in their palm. But their hopes for a better living are belied.

Question 8.
What is the open prayer made by the country folk?
Answer:
The country folk make an open appeal to the city dwellers that they should not be selfish. They expectantly pray for the city cars to stop at their roadside stand and help them lead a better life.

Question 9.
What is the trusting sorrow? What remains unsaid?
Answer:
The country folk trust their rich brethren in the city to come to their help but they feel sad when their trust is breached by the city people through their indifference. Although the city people have said nothing but their silence speaks volumes about their cold and indifferent attitude to the rural poor, who feel hurt by it.

Question 10.
Which things irritated those passers-by who stopped at the roadside stand?
Answer:
The passers-by got irritated by the tastelessly painted roadside stand. The thought that the artless decor of the stand was in disharmony with their surroundings and it had destroyed the scenic beauty of the landscape. Even their ‘N’ and ‘S’ on the signboards was wrongly presented. They did not approve of the things offered for sale.

Question 11.
Why did the people driving along the highway think that the landscape was marred?
Answer:
The people driving along the highway objected to the tastelessly painted roadside stand. They thought that the artless decor of the stand was in disharmony with the surroundings and had destroyed the scenic beauty of the landscape. Although the shed had been recently renovated but it could never impress the city dwellers. They were always critical and felt that these unhygienically maintained roadside stands marred the beautiful mountain scene.

Question 12.
Who actually stopped near the sheds put up by the farmers at the edges of the road?
Answer:
The poet states clearly that three cars stopped but none inquired about the prices of the farmer’s produce. One car stopped to reverse and another asked the way to where it was bound. The third foolishly asked if they could sell it a gallon of gas.

Question 13.
What would be the great relief for the poet in reference to these village folks?
Answer:
The poet says loudly that he would be happy to own the great relief if the pains of these people were removed at one stroke. Obviously, he is much moved by their pathetic plight of life. He wants something to be done to improve their lives economically.

Question 14.
What hope does the poet nurture about himself when he asks that these people should be put at one stroke out of their pain?
Answer:
The poet hopes that these people are put at one stroke out of their pain. The poet wants that the authorities should come to him and offer to put him ‘gently out of my pain’. The poet identifies himself with the village folks as far as their economic conditions are concerned.

Question 15.
What is the poet’s attitude to the good-doers and why is it so?
Answer:
The poet condemns the good-doers for they actually take away the villagers’ freedoms to think for themselves. They force benefits on them which lull them into doing nothing and destroy their peace of mind and their lives. He criticizes them for exploiting the villagers for their own gains.

Question 16.
What different attitudes do the city dwellers display to the country people?
Answer:
The city dwellers are indifferent to the plight of the country people and ignore the stands selling their goods. They get irritated with them for spoiling the landscape with their wrong signboards. They also exploit them for their selfish gains by offering them hollow charity which spoils their lives.

Question 17.
On what occasions do the country people express their anger at the city elite?
Answer:
The country people get angry with the city elite when, despite having money, they do not buy any of their goods. Again when a car stops and asks for gas which they obviously do not have, but does not ask the price of what they are actually selling.

Question 18.
What do the country people want?
Answer:
The country people want a share in the wealth enjoyed by the city people which they also have a right to, so that they can improve their conditions and lead better lives just as those promised by the movies and which the government has denied them.

Question 19.
Why are the country folks disappointed?
Answer:
The country folks have put up a roadside stand to sell their wares to the city dwellers. They desperately hope to earn some city money so that they could support their lives with it. They are disappointed because the city dwellers rush away in their polished cars with their minds focused only on their destination. If ever they pause, they are rather critical in their comments. They complain that the roadside stand had marred the scenic beauty of the landscape.

Question 20.
Bring out the contrast between the urban rich and the rural poor.
Answer:
The urban rich are on the move, they are in a hurry, they are speeding looking ahead. They have no time to inquire about the goods put up by rural poor for sale. On the other hand, the rural poor are standing and pleading for help.

Question 21.
How does the poet describe the double standards of the government and other social service agencies towards the poor rural people?
Answer:
The poet is sad that the government which came into power had many promises for the wellbeing of rural poor folks. But it and other social agencies did nothing for that. These poor rural people put up their roadside stands to sell what they produce. But no passer-by buys them. The poet feels much pain at their poor plight.

NCERT Solutions for Class 12 Physics Chapter 15 Communication Systems

NCERT Solutions for Class 12 Physics Chapter 15 Communication Systems are part of NCERT Solutions for Class 12 Physics. Here we have given. NCERT Solutions for Class 12 Physics Chapter 15 Communication Systems.

Question 1.
At which of the following frequency/frequencies the communication will not be reliable for a receiver situated beyond the horizon:
(a) 10 kHz
(b) 10 MHz
(c) 1 GHz
(d) 1000 GHz
Answer:
(b) is correct. Here (c) and (d) frequencies have high penetration power so the earth will absorb them. Radiation (a) of 10 kHz will suffer from the problem of the size of the antenna.

Question 2.
Frequencies in the UHF range normally propagate by means of
(a) ground waves
(b) sky waves
(c) surface waves
(d) space waves.
Answer:
(d) space waves.

Question 3.
Digital signals (i) do not provide a continuous set of values, (ii) represent values as discrete steps, (Hi) can utilize the only binary system, and (iv) can utilize decimal as well as a binary system. Which of the following options is true :
(a) Only (i) and (ii).
(b) Only (ii) and (iii).
(c) Only (i), (ii) and (iii), but not (iv).
(d) AH the above (i) to (iv).
Answer:
(c) is correct because the decimal system is concerned with continuous values (i) to (iii).

Question 4.
Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81 m tall. How much service area can it cover if the receiving antenna is at the ground level?
Answer:
For line-of-sight communication, it is necessary that the transmitting antenna and receiving antenna should be eye to eye but it is not necessary that they should be at the same height.

Question 5.
A carrier wave of peak voltage 12 V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75%?
Answer:

Question 6.
A modulation signal is a square wave as shown in the figure. The carrier wave is given by
C(t) = 2 sin(8πt) V

(a) Sketch the amplitude modulated waveform.
(b) What is the modulation index?
Answer:


Accordingly, the amplitude modulated waveform is shown ahead:

Question 7.
For an amplitude modulated wave, the maximum amplitude is found to be 10 V while the minimum amplitude is found to be 2 V. Determine the modulation index μ. What would be the value of μ if the minimum amplitude is zero V?
Answer:

Question 8.
Show that if a device is available which can multiply two signals, then it is possible to recover the modulating signal at the receiver station.
Answer:
Let there be two signals represented by
A_c cos ω_ct and A₀ cos(ω_c + ω_m)t where A_c is the
amplitude, ω_c is the angular frequency of a carrier wave at the receiving end and A₀ is the amplitude, (ω_c+ ω_m) is the angular velocity of the modulated wave.
Multiplying these signals, we get

We hope the NCERT Solutions for Class 12 Physics Chapter 15 Communication Systems, help you. If you have any query regarding NCERT Solutions for Class 12 Physics Chapter 15 Communication Systems, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance

NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance are part of NCERT Solutions for Class 12 Physics. Here we have given. NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance

Question 1.
Two charges 5 x 10^-8 C and -3 x 10^-8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero. Ans. Let the potential be zero at 0, then
Answer:
Let the potential be zero at 0, then v_A + V_B= 0, where V_A is electric potential due to charge q_A and V_B is the electric potential due to charge q_B.

Question 2.
A regular hexagon of side 10 cm has a charge 5 μC at each of its vertices. Calculate the potential at the center of the hexagon.
Answer:
Total potential at O is given by,

Question 3.
Two charges 2μC and -2μC are placed at points A and B, 6 cm apart.
(a) Identify an equipotential surface of the system. % What is the direction of the electric field at every through the mid-point. On this plane, the potential is zero everywhere.
(b) The direction of the electric field is from positive to negative charge i.e. A to B, which is in fact perpendicular to the equipotential plane.
Answer:
(a) A surface containing an equatorial line and a perpendicular line.
(b) Towards the side of – ve charge, parallel to the axis.

Question 4.
A spherical conductor of a radius of 12 cm has a charge of 1.6 x 10^-7 C distributed uniformly on its surface. What is the electric field
(a) inside the sphere
(b) just outside the sphere
(c) at a point 18 cm from the center of the sphere?
Answer:
(a) inside a conductor, the electric field is zero because the charge resides on the surface of a conductor.
(b) Electric field just outside the sphere is given by

Question 5.
A parallel plate capacitor with air between the plates has a capacitance of 8 pF
(1 pF = 10^-12 F.) What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
Answer:

Question 6.
Three capacitors each of capacitance 9 pF are connected in series.
(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply ?
Answer:

Question 7.
Three capacitors of capacitances 2 pF, 3 pF and 4pF are connected in parallel.
(a) What is the total capacitance of the combination?
(b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.
Answer:
(a) Total capacitance
= c₁ + c₂ + c₃
= 2 + 3+ 4 = 9pF.
(b) Using C = \(\frac { q }{ v } \) we get q = CV
∴ q_x = C₁V = 2 x 10-¹² x 100
= 2 x 10-¹⁰ C = 200 pC
q₂ = c₂V
= 3 x 10^-12 x 100
= 3 x 10-¹⁰ C = 300 pC
q₃ = c₃v
= 4 x 10-¹² x 100
= 4 x 10-¹⁰ C = 400 pC

Question 8.
In a parallel plate capacitor with air between the plates, each plate has an area of
6 x 10^-3 in² and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor ?
Answer:

Question 9.
Explain what would happen if in the capacitor given in Q. 2.8, a 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates,
(a) while the voltage supply remained connected.
(b) after the supply was disconnected.
Answer:

Question 10.
A 12 pF capacitor is connected to a 50 V battery.How much electrostatic energy is stored in the capacitor ?
Answer:
E = \(\frac { 1 }{ 2 } \) CV² = \(\frac { 1 }{ 2 } \) x 12 x 10-¹² x 50 x 50 = 1.5 2 2 x 10-⁸J.

Question 11.
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from die supply and is connected  to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process ?
Ans.
Here, C₁ = 600pF = 6 x 10^-10 F, C₂ =
6 x 10-¹⁰ F, V₁ = 200V, V₂ = 0

Question 12.
A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of -2 x 10^-9 C from a point P(0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point
R(0, 6 cm, 9 cm.)
Answer:
The work done by electrostatic force on a charge is independent of the path followed by the charge. It depends only on the initial and final positions of the charge.

Question 13.
A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the center of the cube.
Answer:
(1) Distance of the center of the cube from vertex is half of the diagonal of the cube

(2) From symmetry, it is clear that electric field at center of the cube is zero.

Question 14.
Two tiny spheres carrying charges 1.5 μc and 2.5 μc are located 30 cm apart. Find the potential and electric field :
(a) at the mid point of the line joining the two charges,
(b) at a point 10 cm from this mid-point in a plane normal to the line and passing through the mid­point.
Answer:

Question 15.
A spherical conducting shell of inner radius r_l and outer radius r₂ has a charge Q.
(a) A charge q is placed at the center of the shell. What is the surface charge density on the inner and outer surfaces of the shell?
(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.
Answer:
(a) Charge Q appears on the outer surface.

When charge q is placed at the center, it induces – q charge on the inner surface and +q on the outer surface.
.’. charge density of the inner surface,

and charge density of the outer surface,

Consider a cavity of an irregular shape with the net charge to be zero inside it. Let a closed-loop be partially inside and the rest outside the cavity. The field inside the conductor is zero, so some work is done by the field to carry a test charge in the closed-loop, but this is against the provisions of an electrostatic field because as per Gauss’s law, the net charge inside a Gaussian surface must be zero. Thus, there cannot be field lines inside the cavity irrespective of its shape.

Question 16.
(a) Show that the normal component of the electrostatic field has a discontinuity from one side of a charged surface to another given by

where \(\hat { n } \) is a unit vector normal to the surface at a point and a is the surface charge density at that point. (The direction of h is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is σ\(\hat { n } \) /ε₀
(b) Show that the tangential component of the electrostatic field is continuous from one side of a charged surface to another.[Hint. For (a), use Gauss’s law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]
Answer:
Consider a sheet of charge having charge density a. E on either side of the sheet, perpendicular to the plane of sheet, has same magnitude at all points equidistant from the sheet.
Electric field intensity on the left side of the sheet,

The electric field tangential to the plate is continuous throughout.

Question 17.
a long charged cylinder of linear charged density A. is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?
Answer:
A cylinder P has linear charge density, λ, length l, and radius r₁
The charge on cylinder P, q = XL A hollow co-axial conducting cylinder of length / and radius r₂ surrounds the cylinder P. Charge on cylinder Q = – q.

Consider a Gaussian surface in the form of a cylinder of radius r and length l. The electric flux through the curved surface of the Gaussian surface,

Question 18.
In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å:
(a) Estimate the potential Energy of the system in eV, taking the zero of the potential energy at an infinite separation of the electron from the proton.
(b) What is the minimum work required to free the electron, given that it’s kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?
(c) What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06 A separation?
Answer:

Question 19.
If one of the two electrons of an H₂ molecule is removed, we get a hydrogen molecular ion H⁺₂. In the ground state of an H⁺₂, the two protons are separated by roughly 1.5 Å, and the electron is roughly Å from each proton. Determine the potential energy of the system. Specify your choice of zero potential energy.
Answer:

Question 20.
Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of the electric field at the surfaces of the two spheres? Use the result obtained to explain why the charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.
Answer:
Two charged conducting spheres of radii a and b connected by a wire will reach to the same potential.

Clearly, electric charge density for the pointed surface will be more because a flat surface can be equated to a spherical surface of large radius and a pointed portion to a spherical surface of small radius.

Question 21.
Two charges -q and + q are located at points (0, 0, -a) and (0, 0, a), respectively.
(a) What is the electrostatic potential at the points (0, 0, z) and (x, y, 0)?
(b) Obtain the dependence of potential on the distance r of a point from the origin when r/a > > 1.
(c) How much work is done in moving a small test charge from the point (5, 0, 0) to (-7, 0, 0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?
Answer:

The point (x, y, 0) is perpendicular to Z-axis, there­fore, the potential at (x, y, 0) is zero.
(b) Consider P to be the point of observation at a distance r from the center (O) of the electric dipole.
Let OP make an angle 0 with the dipole moment \( \overrightarrow { p } \)
and r_1, r₂ be the distances of point P from – q charge and + q charge respectively. Potential at P due to – q charge,



The answer does not change because, in electrostatics, the work done does not depend upon the actual path, it simply depends upon the initial and final positions.

Question 22.
The figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a > > l, and contrast your results with that due to an electric dipole, and an electric monopole
(i.e., a single charge.)

Answer:

(2) Due to electric dipole, the potential is of 1/r² type.
(3) Due to an electric monopole, the potential is of 1/r type.

Question 23.
An electrical technician requires a capacitance of 2 μF in a circuit across a potential difference of 1 kV. A large number of 1 μF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.
Answer:
Let N capacitors be used in m rows when each row has n capacitor i.e. N = mn
In series

Question 24.
What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between the plates is 0.5 cm ? (You will realise from your answer why ordinary capacitors are in the range of μF or less. However, electrolytic capacitors do have a much larger capacitance ((0.1 F) because of very minute separation between the conductors.)
Answer:

Question 25.
Obtain the equivalent capacitance of the network in figure. For a 300 V supply, determine the charge and voltage across each capacitor. (C.B.S.E. 2008)

Answer:
The equivalent circuit is as shown below :

Potential difference across C₄ is in the ratio 2:1
i.e., 200 V
.’. Charge on C₄ = C₄V₄
= 100 x 200 x 10^-12 = 2 x 10^-8 C
Potential difference across C₁= 100 V
Charge on C₁ = C₁x V₁
=100 x 100 x 10-¹² = 1 x 10^-8 C
Potential difference across C₂ and C₃ is 50 v each
∴ Charge on C₂ or C₃ = C₂V₂
= 200 x 50 x 10^-12 = 10-⁸ C.

Question 26.
The plates of a parallel plate capacitor have an area of 90 cm² each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply.
(a) How much electrostatic energy is stored by the capacitor?
(b) View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume Hence arrive at a relation between u and the magnitude of electric field E between the plates.
Answer:

Question 27.
A 4 μF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 μF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?
Answer:

Question 28.
Show that the force on each plate of a parallel plate capacitor has a magnitude equal to (1/2) QE, where Q is the charge on the capacitor and E is the magnitude of the electric field between the plates. Explain the origin of the factor (1/2).
Answer:
Let F be the force on each plate of the capacitor. If the distance between the plates of the capacitor is increased by dx, then work done = F dx. This work done is stored as the potential energy of the capacitor. The increase in the volume of capacitor = A dx

Question 29.
A spherical capacitor consists of two concentric spherical conductors held in position by suitable insulating supports (Figure.) Show that the capacitance of a spherical capacitor is given by

where r_x and r₂ are the radii of outer and inner spheres, respectively.
Answer:
It consists of two concentric spherical shells A and B of radii a and b with charge +q and charge -q respectively. (Outer sphere is grounded)

Question 30.
A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 pC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
Answer:

Question 31.
Answer carefully:
(a) Two large conducting spheres carrying charges Q₁ and Q₂ are brought close to each other. Is the magnitude of the electrostatic force between them exactly given by Q₁Q₂/4Πε₀r², where r is the distance between their centers?
(b) If Coulomb’s law involved 1/r³ dependence (instead of 1/r²), would Gauss’s law be still true?
(c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
(d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?
(e) We know that the electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?
(f) What meaning would you give to the capacitance of a single conductor?
(g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (=6).
Answer:
(a) No. The given relation is Coulomb’s law which is true for point charges. In the present case, as the spheres are brought closer, the distribution of charge on them becomes nonuniform.

(b) No. The surface area in space varies as r₂ so that field varies as \(\frac { 1 }{ { r }^{ 2 } }\). Hence \(\frac { 1 }{ { r }^{ 2 } }\) dependence is essential.

(c) Not necessarily. The motion of charged particles need not be along the line of the field. It does so in the uniform field. The field gives the direction of acceleration and not that of velocity in general.

(d) Zero. For any complete path in the electrostatic field (the shape does not matter), it is zero.

(e) No. Potential is continuous there.

(f) The single conductor can form a condenser with the other conductor at infinity. Hence the meaning of storage of charge retains.

(g) Water molecules are polar molecules.

Question 32.
A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 pC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects, (i.e., bending of field lines at the end)
Answer:
The capacitance of a cylindrical capacitor is given by


Question 33.
A parallel plate capacitor is to be designed with a voltage rating of 1 kV, using a material of dielectric constant 3 and dielectric strength of about 10⁷ Vm^-1. (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionization.) For safety, we should like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50 pF?
Answer:
10% of the given field i.e. 10⁷ V m¹ gives E = 0.1 X 10⁷ Vnr¹

Question 34.
Describe schematically the equipotential surfaces corresponding to
(a) a constant electric field in the z-direction,
(b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction,
(c) a single positive charge at the origin, and
(d) a uniform grid consisting of long equally spaced parallel charged wires in a plane.
Answer:
(a) A plane parallel to XY plane.
(b) Plane parallel to XY plane but the planes having different fixed potential will become closer with the increase in field intensity.
(c) Concentric spheres with origin as the center.
(d) A time-dependent changing shape nearer to the grid which slowly becomes planar and parallel to the grid at far off distances from the grid.

Question 35.
In a van de Graaff type generator a spherical metal shell is to be a 15 X 10⁶ V electrode. The dielectric strength of the gas surrounding the electrode is 5 x 10⁷ vm^-1. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.) (C.B.S.E. 2008)
Answer:
The minimum radius of the shell of the van de Graaff generator is given by the relation

Question 36.
A small sphere of radius r₁ and charge q₁ is enclosed by a spherical shell of radius r₂ and charge q₂ . Show that if q₁ is positive, the charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge
q₂ on the shell is.
Answer:
Charge resides on the outer surface of a conductor. So the charge on the inner sphere will flow towards the shell through the conducting wire. Moreover, from Gauss’s law, no electric field exists inside a Gaussian surface, and also the charges enclosed by a closed surface only contribute towards the field. So q₂ does not matter in this case. It is positive, a potential difference is also positive.

Question 37.
Answer the following:
(a) The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decrases with altitude. Near the surface of the earth, the field is about 100 Vm^_1. Why then do we not get an electric shock as we step out of our house into the open ? (Assume the house to be a stell cage so there is no field inside !)
(b) A man fixes outside his house one evening a two meter high insulating slab carrying on its top a large aluminium sheet of area 1 m². Will he get an electric shock if he touches the metal sheet next morning ?
(c) The discharging current in the atmosphere due to the small conductivity of air is known to be 1800 A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral ? In other words, what keeps the atmosphere charged ?
(d) What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning ?
[Hint. The earth has an electric field of about 100 Vm^-1 at its surface in the downward direction, corresponding to a surface charge density = -10^-9 C m^-2. Due to the slight conductivity of the atmosphere up to about 50 km (beyond which it is good conductor), about +1800 C is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.]
Answer:
(a) Our body and the ground form an equipotential surface. As we step out into the open, the original equipotential surfaces of open-air change, keeping our head and the ground at the same potential.

(b) Yes. The steady discharging current in the atmosphere charges up the aluminum sheet gradually and raises its voltage to an extent depending on the capacitance of the capacitor (formed by the sheet, slab, and the ground).

(c) The atmosphere is continually being charged by thunderstorms and lightning all over the globe and discharged through regions of ordinary weather. The two opposing currents are, on average, in equilibrium.

(d) Light energy involved in lightning; heat and sound energy in the accompanying thunder.

We hope the NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance, help you. If you have any query regarding NCERT Solutions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 12 History Chapter 13 Mahatma Gandhi and the Nationalist Movement Civil Disobedience and Beyond are part of NCERT Solutions for Class 12 History. Here we have given NCERT Solutions for Class 12 History Chapter 13 Mahatma Gandhi and the Nationalist Movement Civil Disobedience and Beyond.

NCERT Solutions for Class 12 History Chapter 13 Mahatma Gandhi and the Nationalist Movement Civil Disobedience and Beyond

Question 1.
How did Mahatma Gandhi seek to identify with the common people ?
Solution :
Mahatma Gandhi was appreciated by the people because he dressed like them, lived like them, and spoke their languages. He tried to identify with them in the following ways :

• Gandhiji dressed himself in simple dhoti or loin cloth.
• He spent part of each day working on the charkha (spinning wheel) and encouraged other nationalists to do likewise.
• His new appearance i.e., shaved head and wearing a loincloth, came to symbolise asceticism and abstinence – the qualities he had in opposition to the consumerist culture of the modem world.

Question 2.
How was Mahatma Gandhi perceived by the peasants?
Solution :
India is a country of villagers and vast number of Indians are engaged in farming. Mahatma Gandhi knew that during freedom struggle his focus was to address the issues of farmers. He dressed like farmers. His involvement in Indian politics began in Champaran when he successfully resolved the issues of farmers. He stood for farmers against excesses of the British government like high taxes and oppressive tax collections.
Apart from all the above, mystery also surrounded the personality of Mahatma Gandhi. Many believed he was endowed with supernatural powers. Stories spread that those who spoke ill of Mahatma Gandhi suffered natural calamities.
Thus, farmers perceived Mahatma Gandhi as their saviour and still many believed he was bestowed with the power to perform miracles.

Question 3.
Why did the salt laws become an important issue of struggle ?
Solution :

1. The salt laws became an important issue of stmggle because these laws gave the state a monopoly in the manufacture and sale of salt.
2. For in every Indian household, salt was indispensable, yet people were forbidden from making salt even for domestic use, compelling them to buy from shops at a high price.
3. The salt tax at times was even fourteen times its value.
4. According to Gandhiji, the government not only prevented the public from manufacturing but also destroyed what nature manufactured without effort. The salt officers were posted for carrying on destruction of natural salt.
5. Gandhiji stated that the salt monopoly was a fourfold curse :
   • It deprived the people of a valuable easy village industry,
   • It involved wanton destruction of property that nature produced in abundance,
   • Its destruction meant more national expenditure, and
   • Tax of more than 1000 per cent was exacted from a starving people.

Question 4.
Why are newspapers an important source for the study of the national i movement ?
Solution :
Newspapers, published in English as well as in the different Indian languages are important contemporary sources because they tell us about daily movements of leaders. They report on their activities and their views. Newspapers publish the views of the ordinary people in different parts of the country and the ways in which they participate in the various movements. The newspapers tell us about the objectives of the people and their expectations from their leaders. The newspapers publish all types of views which are generally different from each other. For example, a newspaper published in London gave the view point and reaction of the British public while an Indian newspaper gave the reaction of the people of India. Thus, newspapers are an important source for the study of the national movement.

Question 5.
Why was the charkha chosen as a symbol of nationalism?
Solution :
Gandhiji used to work on charkha. He made it a symbol of our freedom movement. Following are the reasons for making it the symbol of our freedom struggle.
(a) Charkha symbolised manual labour.
(b) Gandhiji wanted to attach respect to manual labour. On charkha people worked with their own hand.
(c) Charkha was a low investment product hence anyone can afford it. It was a boost to the small scale industries.
(d) Charkha as it dignified manual labour. It also promoted the culture of doing one’s own work. It would also strike at the root of caste system.
(e) Charkha was used as tool to keep British imported clothes. Thus, Charkha became a symbol of Indian nationalism.

Question 6.
How was non-cooperation a form of protest?
Solution :
Non-cooperation was a form of protest in the following ways :

1. Indians were asked to adhere to a “renunciation of all voluntary association with the government to end colonialism”.
2. Gandhiji had joined hands with the Khilafat Movement to restore the Caliphate, a symbol of Pan-Islamism which had been abolished. It was also hoped that Britain would impose a harsh treaty on Turkey after its defeat in World War I.

Thus, it was a protest against the British policies in India and towards Turkey. Gandhiji hoped that if non-cooperation was effectively carried out, India would win Swaraj within a year.

Question 7.
Why were the dialogues at the Round Table Conference inconclusive?
Solution :
The dialogues at the Round Table Conference were inconclusive due to the following factors :

1. The First Conference was held in November 1930 when the Civil Disobedience Movement was being organised by the Congress. So, none of its leaders was present in the conference and without Congress participation it could not succeed.
2. Second Round Table Conference was held in the latter part of 1931. Gandhiji represented as the sole representative of

Congress. But his representation was challenged by the Muslim League, the Princes, and B.R. Ambedkar.
Under these circumstances, the Conference was inconclusive and could not take any decision.

Question 8.
In what way did Mahatma Gandhi transform the nature of the national movement?
Solution :
Before Gandhiji came to India, the national movement was limited to few sections of society. During the Swadeshi Movement of 1905-07, Bal Gangadhar Tilak, Bipin Chandra Pal and Lala Lajpat Rai tried to make it an all-India phenomenon but even then the participation of ordinary people remained limited. In his speech at Banaras in February, 1916, even Gandhi said that Indian nationalism was an elite phenomenon – a creation of lawyers, doctors and landlords. He reminded that the peasants and workers were not represented there. He desired to make Indian nationalism more properly representative of the Indian people as a whole. And thereafter whenever he got a chance he tried to implement his desire into action. Thus, in 1917 and 1918, he took initiatives at Champaran, Ahmedabad and Kheda which marked Gandhiji as a nationalist with a deep sympathy for poor.

In 1919, he called for a countrywide campaign against the “Rowlatt Act”. The campaign in the Punjab led to Jallianwala Bagh massacre. This satyagraha made Gandhiji a truly nationalist leader. Gandhiji was encouraged by the success of these satyagrahas and decided to start “non¬cooperation” movement which totally changed the nature of the national movement because it was the first mass movement in which all classes of people — students, lawyers, peasants, etc. took part. Thus, by 1922 he had transformed Indian nationalism, thereby redeeming the promise he made in his BHU speech of February 1916. It was no longer a movement of professionals and intellectuals but of hundreds of thousands of peasants, workers and artisans.

Question 9.
What do private letters and autobiographies tell us about an individual? How are these sources different from official accounts ?
Solution :
(a)

• Private letters give us a glimpse of individual’s thoughts.
• In letters, a person expresses his anger and pain, his dismay and anxiety, his hopes and frustrations in ways in which he may not express himself in public statements.
• Sometimes an individual cannot express his opinion in letters due to fear that a letter may be printed in future.

(b)

• Autobiographies give us an account of the past of the individual. It is often rich in human detail.
• Autobiographies tell us what an individual recollect from his memory. It could be important from the point of view of an individual.

(c) These sources – private letters and autobiographies – are different from official accounts because private letters and autobiographies are written according to the wishes of an individual. On the other hand, official accounts are written while performing official duty. These represents the view point of the government. For example, the fortnightly reports that were prepared by the Home Department were based on police information and expressed what the higher officials saw or wanted to believe.

We hope the NCERT Solutions for Class 12 History Chapter 13 Mahatma Gandhi and the Nationalist Movement Civil Disobedience and Beyond help you. If you have any query regarding NCERT Solutions for Class 12 History Chapter 13 Mahatma Gandhi and the Nationalist Movement Civil Disobedience and Beyond, drop a comment below and we will get back to you at the earliest.