Question

A number of spherical conductors of different radii have same potential. Then the surface
charge density on them:
(a) are equal
(b) is proportional to the square of their radii
(c) is proportional to their radii
is inversely proportional to their radii
(d) is proportional to their radii ​

Answer 1

Answer:

We know voltage on a spherical conductor is given by V=

R

Kq

where q is the charge on that sphere and K=

4πϵ

o

1

.

⇒q=

K

VR

Let R be the radius of that sphere.

Now surface charge density is σ=

A

q

=

4πR

2

q

∴ σ=

K4πR

2

VR

=

4πRK

V

⟹ σ∝

R

1

Hence option B is correct.