ELECTRIC CHARGES AND FIELDS

1. 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?
2. What is the force between two small charged spheres having charges of 2 × 10 –7 C and 3
× 10 –7 C placed 30 cm apart in air?
3. 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 0.2N.(a) What is the distance between the two spheres?(b) What is
the force on the second sphere due to the first?
4. Four point charges q A = 2 µC, q B = – 5 µC, q C = 2 µC and q D = – 5 µC are located at
the corners of a square ABCD of side10 cm. What is the force on a charge of 1 µC placed at
the centre of the sphere?
5. (a) Two insulated charged copper spheres A and B have their centres separated by a
distance of 50 cm. What is the mutual force of electrostatic 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?
6. Suppose the spheres A and B in above question 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?
7. Two-point charges q A = + 3 µC and q B = – 3 µC are located 20 cm apart in vacuum. (a)
What is the electric field at the mid-point O of the line AB joining the two charges? (b) If a
negative test charge of magnitude 1.5×10 –9 C is placed at this point, what is the force
experienced by the test charge?
8. A system has two charges q A = 2.5 × 10 –7 C and q B = – 2.5 × 10 –7 C located at points
A = (0, 0, –15 cm) and B = (0, 0, +15cm) respectively. What are the total charge and electric
dipole moment of the system?
9. An electric dipole with a dipole moment 4 × 10 –9 Cm is aligned at 30° with the direction
of a uniform electric field of magnitude 5 × 10 4 NC –1 Calculate the magnitude of the torque
acting on the dipole.
10. A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm
from the centre of sphere is1.5 × 10 3 NC –1 and points radially inward, what is the net
charge on the sphere?
11. An infinite line charge produces an electric field of 9 × 10 4 NC –1 at a distance of 2 cm.
Calculate the linear charge density.
12. An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55
× 10 4 NC –1 in Millikan’s oildrop experiment. The density of the oil is 1.26 g cm –3 .
Estimate the radius of the drop (g = 9.81 ms –2 ; e = 1.60 × 10 –19 C)
13. Consider a uniform electric field E = 3 × 10 3 i NC -1
1. Which statement among the following is false regarding Gauss’s law?
(a) Gauss’s law holds for any closed surface.
(b) In Gauss’s law, the term “q” on the right side of the equation represents the total charge
enclosed within the surface.
(c) When a system exhibits symmetry, Gauss’s law may not be beneficial for calculating the
electrostatic field.
(d) Gauss’s law is derived from Coulomb’s law, which contains an inverse square
dependence on distance.

2. Assume a system inside which there are different types of charges, but the total charge is
practically zero. At points outside the given region
(a) the electric field must be zero.
(b) the electric field is caused solely by the dipole moment of the charge distribution.
(c) For large distances (r) from the origin, the dominant electric field is inversely proportional
to r3.
(d) if a charged particle is moved along a closed path away from a region, the work done will
not be zero.

3. The quantisation of charge implies that

(a) it is not possible for a charge to be a fraction of the charge on an electron.
(b) charges cannot be destroyed
(c) charge exists on particles, and there is a minimum allowable charge for a particle.

4.If a parrot sits on a bare high-voltage power line, it will:

(a) receive a mild shock
(b) receive a strong shock
(c) be killed instantly
(d) not be affected significantly.

5. If two conducting spheres are charged separately and then connected, the following may
occur:
(a) The electrostatic energy of the spheres will be conserved.
(b) the total charge on the spheres is conserved
(c) Both the electrostatic energy and charge will be conserved.
(d) None of the above.

1) Which orientation of an electric dipole in a uniform electric field would correspond to

stable equilibrium ?
2) If the radius of the Gaussian surface enclosing a charge is halved, how does the electric
flux through the Gaussian surface change?

3) which orientation, a dipole placed in a uniform electric field is in

 stable,
 unstable equilibrium?

4) Figure shows three-point charges, +2q, -q and + 3q. Two charges +2q and -q are enclosed
within a surface ‘S’. What is the electric flux due to this configuration through the surface ‘S’
(Delhi 2010)

5) Name the physical quantity whose S.I. unit is JC-1. Is it a scalar or a vector quantity?

6) Define electric dipole moment. Write its S.I. unit.

7) Why should electrostatic field be zero inside a conductor?

8) Why must electrostatic field be normal to the surface at every point of a charged
conductor?
9) A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing
through each face of the cube?

10) A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing
through two opposite faces of the cube? (All India)

11) Why do the electric field lines not form closed loops?
12) Is the electric field due to a charge configuration with total charge zero, necessarily zero?
Justify.
13) Two charges of magnitudes – 2Q and + Q are located at points (a, 0) and (4a,0)
respectively. What is the electric flux due to these charges through a sphere of radius ‘3a’
with its centre at the origin?

14) A point charge +Q is placed in the vicinity of a conducting surface. Draw the electric
field lines between the surface and the charge.
15) Derive an expression for the torque experienced by an electric dipole kept in a uniform
electric field. (Delhi 2017)
16) electric flux. Write its S.I. unit.

17) A spherical conducting shell of inner radius rx and outer radius r2 has a charge ‘Q’. A
charge ‘q’ is placed at the centre of the shell.
(a) What is the surface charge density on the
(i) inner surface,
(ii) outer surface of the shell?
18) Given a uniform electric field E→ = 2 × 103 i^ N/ C, find the flux of this field through a
square of side 20 cm, whose plane is parallel to the y-z plane. What would be the flux
through the same square, if the plane makes an angle of 30° with the x-axis?

19) Given a uniform electric field E→=4×103i^ N/C. Find the flux of this field through a
square of 5 cm on a side whose plane is parallel to the Y-Z plane. What would be the flux
through the same square if the plane makes a 30° angle with the x-axis?

20)A small metal sphere carrying charge +Q is located at the centre of a spherical cavity in a
large uncharged metallic spherical shell. Write the charges on the inner and outer surfaces of
the shell. Write the expression for the electric field at the point P1
21) the term ‘electric flux’. Write its S.I. units. What is the flux due to electric
field E→=3×103 N/C through a square of side 10 cm, when it is held normal to if?

22) thin conducting spherical shell of radius R has charge Q spread uniformly over its
surface. Using Gauss’s law, derive an expression for an electric field at a point outside the
shell.
e point lies on it.

23) State Gauss’ law in electrostatics. Using this law derive an expression for the electric
field due to a uniformly changed infinite plane sheet.
24) State ‘Gauss law’ in electrostatics. Use this law to derive an expression for the electric
field due to an infinitely long straight wire of linear charge density λ cm-1
of the curved surface S1 and is directed radially outward.
25) An electric dipole of dipole moment p→ is placed in a uniform electric field E→?.
Obtain the expression for the torque τ→experienced by the dipole. Identify two pairs of
perpendicular vectors in the expression.
26) (i) Derive the expression for electric field at a point on the equatorial line of an electric
dipole.
(ii) Depict the orientation of the dipole in
(a) stable,
(b) unstable equilibrium in a uniform electric field.