NCERT Solutions Class 12 Physics Chapter 1 Electric Charges And Fields Download In Pdf

Chapter 1 Electric Charges and Fields Download in pdf

**Question 1.1** What is the force between two small charged spheres having
charges of 2 × 10–7C and 3 × 10–7C placed 30 cm apart in air?

**Question 1.2** The electrostatic force on a small sphere of charge 0.4 μC due to
another small sphere of charge – 0.8 μC in air is 0.2 N.

(a) What is
the distance between the two spheres?

(b) What is the force on the
second sphere due to the first?

**Question 1.3** Check that the ratio ke2/G memp is dimensionless. Look up a Table
of Physical Constants and determine the value of this ratio. What
does the ratio signify?

**Question 1.4** (a) Explain the meaning of the statement ‘electric charge of a body
is quantised’.
(b) Why can one ignore quantisation of electric charge when dealing
with macroscopic i.e., large scale charges?

**Question 1.5** When a glass rod is rubbed with a silk cloth, charges appear on
both. A similar phenomenon is observed with many other pairs of
bodies. Explain how this observation is consistent with the law of
conservation of charge.

**Question 1.6** Four point charges qA = 2 μC, qB = –5 μC, qC = 2 μC, and qD = –5 μC are
located at the corners of a square ABCD of side 10 cm. What is the
force on a charge of 1 μC placed at the centre of the square?

**Question 1.7** (a) An electrostatic field line is a continuous curve. That is, a field
line cannot have sudden breaks. Why not?
(b) Explain why two field lines never cross each other at any point?

**Question 1.8** Two point charges qA = 3 μC and qB = –3 μC are located 20 cm apart
in vacuum.

(a) What is the electric field at the midpoint O of the line AB joining
the two charges?

(b) If a negative test charge of magnitude1.5 × 10–9 C is placed at
this point, what is the force experienced by the test charge?

**Question 1.9** A system has two charges qA = 2.5 × 10–7 C and qB = –2.5 × 10–7 C
located at points A: (0, 0, –15 cm) and B: (0,0, +15 cm), respectively.
What are the total charge and electric dipole moment of the system?

**Question 1.10** An electric dipole with dipole moment 4 × 10–9 C m is aligned at 30°
with the direction of a uniform electric field of magnitude 5 × 104 NC–1.
Calculate the magnitude of the torque acting on the dipole.

**Question 1.11** A polythene piece rubbed with wool is found to have a negative
charge of 3 × 10–7 C.

(a) Estimate the number of electrons transferred (from which to
which?)

(b) Is there a transfer of mass from wool to polythene?

**Question 1.12** (a) Two insulated charged copper spheres A and B have their centres
separated by a distance of 50 cm. What is the mutual force ofelectrostatic repulsion if the charge on each is 6.5 × 10–7 C? The
radii of A and B are negligible compared to the distance of
separation.

(b) What is the force of repulsion if each sphere is charged double
the above amount, and the distance between them is halved?

**Question 1.13** Suppose the spheres A and B in Exercise 1.12 have identical sizes.
A third sphere of the same size but uncharged is brought in contact
with the first, then brought in contact with the second, and finally
removed from both. What is the new force of repulsion between A
and B?

**Question 1.14** Figure1.33 shows tracks of three charged particles in a uniform
electrostatic field. Give the signs of the three charges. Which particle

**Question 1.15** Consider a uniform electric field E = 3 × 103 î N/C. (a) What is the
flux of this field through a square of 10 cm on a side whose plane is
parallel to the yz plane? (b) What is the flux through the same
square if the normal to its plane makes a 60° angle with the x-axis?

**Question 1.16** What is the net flux of the uniform electric field of Exercise 1.15
through a cube of side 20 cm oriented so that its faces are parallel
to the coordinate planes?

**Question 1.17** Careful measurement of the electric field at the surface of a black
box indicates that the net outward flux through the surface of the
box is 8.0 × 103 Nm2/C. (a) What is the net charge inside the box?
(b) If the net outward flux through the surface of the box were zero,
could you conclude that there were no charges inside the box? Why
or Why not?

**Question 1.18** A point charge +10 μC is a distance 5 cm directly above the centre
of a square of side 10 cm, as shown in Fig. 1.34. What is the
magnitude of the electric flux through the square? (Hint: Think of

**Question 1.19** A point charge of 2.0 μC is at the centre of a cubic Gaussian
surface 9.0 cm on edge. What is the net electric flux through the
surface?

**Question 1.20 **A point charge causes an electric flux of 1.10 × 103 Nm2/C to pass
through a spherical Gaussian surface of 10.0 cm radius centred on
the charge.

(a) If the radius of the Gaussian surface were doubled,
how much flux would pass through the surface?

(b) What is the
value of the point charge?

**Question 1.21 **A conducting sphere of radius 10 cm has an unknown charge. If
the electric field 20 cm from the centre of the sphere is 1.55 × 103 N/C
and points radially inward, what is the net charge on the sphere?

**Question 1.22** A uniformly charged conducting sphere of 2.4 m diameter has a
surface charge density of 80.0 μC/m2.

(a) Find the charge on the
sphere.

(b) What is the total electric flux leaving the surface of the
sphere?

**Question1.23** An infinite line charge produces a field of 9 × 104 N/C at a distance
of 2 cm. Calculate the linear charge density.

**Question1.24** Two large, thin metal plates are parallel and close to each other. On
their inner faces, the plates have surface charge densities of opposite
signs and of magnitude 17.0 × 10–22 C/m2. What is E: (a) in the outer
region of the first plate, (b) in the outer region of the second plate,

ADDITIONAL EXERCISES QUESTIONS

**Question1.25** An oil drop of 12 excess electrons is held stationary under a constant
electric field of 2.55 × 104 NC–1 in Millikan’s oil drop experiment. The
density of the oil is

**Question1.26** g cm–3. Estimate the radius of the drop.
(g = 9.81 m s–2; e =1.60 × 10–19 C).1.26 Which among the curves shown in Fig.1.35 cannot possibly
represent electrostatic field lines?

**Question1.27** In a certain region of space, electric field is along the z-direction
throughout. The magnitude of electric field is, however, not constant
but increases uniformly along the positive z-direction, at the rate of
105 NC–1 per metre. What are the force and torque experienced by a
system having a total dipole moment equal to 10–7 Cm in the negative
z-direction ?

**Question1.28** (a) A conductor A with a cavity as shown in Fig.1.36(a) is given a
charge Q. Show that the entire charge must appear on the outer
surface of the conductor.

(b) Another conductor B with charge q is
inserted into the cavity keeping B insulated from A. Show that the
total charge on the outside surface of A is Q + q [Fig.1.36(b)].

(c) A
sensitive instrument is to be shielded from the strong electrostatic
fields in its environment. Suggest a possible way.

**Question1.29** A hollow charged conductor has a tiny hole cut into its surface.
Show that the electric field in the hole is (σ/2ε0) ˆn , where ˆn is the
unit vector in the outward normal direction, and σ is the surface
charge density near the hole.

**Question1.30** Obtain the formula for the electric field due to a long thin wire of
uniform linear charge density λ without using Gauss’s law. [Hint:
Use Coulomb’s law directly and evaluate the necessary integral.]

**Question1.31** It is now believed that protons and neutrons (which constitute nuclei
of ordinary matter) are themselves built out of more elementary units
called quarks. A proton and a neutron consist of three quarks each.
Two types of quarks, the so called ‘up’ quark (denoted by u) of charge
+ (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e,
together with electrons build up ordinary matter. (Quarks of other
types have also been found which give rise to different unusual
varieties of matter.) Suggest a possible quark composition of a
proton and neutron.

**Question1.32** (a) Consider an arbitrary electrostatic field configuration. A small
test charge is placed at a null point (i.e., where E = 0) of the
configuration. Show that the equilibrium of the test charge is
necessarily unstable.

(b) Verify this result for the simple configuration of two charges of
the same magnitude and sign placed a certain distance apart.

**Question1.33** A particle of mass m and charge (–q) enters the region between the
two charged plates initially moving along x-axis with speed vx (like
particle 1 in Fig.1.33). The length of plate is L and an uniform
electric field E is maintained between the plates. Show that the
vertical deflection of the particle at the far edge of the plate is
qEL2/(2m vx
2).
Compare this motion with motion of a projectile in gravitational field
discussed in Section 4.10 of Class XI Textbook of Physics.

**Question1.34** Suppose that the particle in Exercise in 1.33 is an electron projected
with velocity vx = 2.0 × 106 m s–1. If E between the plates separated
by 0.5 cm is 9.1 × 102 N/C, where will the electron strike the upper
plate? (|e|=1.6 × 10–19 C, me = 9.1 × 10–31 kg.)

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- Chapter 1 Electric Charges and Fields
- Chapter 2 Electrostatic Potential and Capacitance
- Chapter 3 Current Electricity
- Chapter 4 Moving Charges and Magnetism
- Chapter 5 Magnetism and Matter
- Chapter 6 Electromagnetic Induction
- Chapter 7 Alternating Current
- Chapter 8 Electromagnetic Waves
- Chapter 9 Ray Optics and Optical Instruments
- Chapter 10 Wave Optics
- Chapter 11 Dual Nature of Radiation and Matter
- Chapter 12 Atoms
- Chapter 13 Nuclei
- Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits
- Chapter 15 Communication Systems

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