Question

A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C 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 centre of the sphere?

Answer 1

Given: The radius of a spherical conductor is 12 cm and the charge on its surface is 1.6× 10 −7  C.

(a)

As the charge is distributed uniformly only on the surface of the spherical conduct, the electric field inside the spherical conductor will be zero.

Thus, electric field inside the spherical conductor is zero

(b)

The electric field just outside the conductor is given as,

E= q 4π ε 0 r 2

where, electric field just outside the conductor is E, the uniformly distributed charge over the spherical conductor is q, permittivity of free space is ε 0 radius of the sphere is r.

By substituting the given values in the above equation, we get

E= 9× 10 9 ×1.6× 10 −7 [ 12 cm×( 1 m 100 cm ) ] 2 = 10 5   NC −1

Thus, the electric field just outside the sphere is 10 5   NC −1 .

(c)

The electric field at some distance from the centre of the conductor is given as,

E= q 4π ε 0 d 2

where, electric field just outside the conductor is E , the uniformly distributed charge over the spherical conductor is q , permittivity of free space is ε 0 distance of point from the centre of the sphere is d.

By substituting the given values in the above equation, we get

E= 9× 10 9 ×1.6× 10 −7 [ 18 cm×( 1 m 100 cm ) ] 2 =4.4× 10 4   NC −1

Thus, the electric field at a point 18 cm from the centre of the sphere is 4.4× 10 4   NC −1 .