Question

A metallic sphere of radius 2.0 cm is charged with +5.0-μC+5.0-μC charge, which spreads on the surface of the sphere uniformly. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell, of inner radius 5.0 cm and outer radius 6.0 cm. Now, a charge of −5.0-μC−5.0-μC is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell. If potential is zero at infinity, what is the potential of (a) the spherical shell, (b) the sphere, (c) the space between the two, (d) inside the sphere, and (e) outside the shell?

Answer 1

Answer:

Explanation:

Potential due to a charged metallic sphere having charge Q and radius r on its surface will be

v = k Q / r . On the surface and inside the metallic sphere , potential is the same . Outside the sphere , at a distance R from the centre  potential is

v = k Q / R

a ) On the surface of the shell , potential due to positive charge is

V₁ = $\frac{9\times10^9\times5\times10^{-6}}{6\times10^{-2}}$

On the surface of the shell , potential due to negative  charge is

V₁ = $\frac{- 9\times10^9\times5\times10^{-6}}{6\times10^{-2}}$

Total potential will be zero . they will cancel each other.

b ) On the surface of the sphere potential

= $\frac{9\times10^9\times5\times10^{-6}}{2\times10^{-2}}$

= 22.5 x 10⁵ V

On the surface of the sphere potential due to outer shell

= $\frac{9\times10^9\times5\times10^{-6}}{5\times10^{-2}}$

= -9 x 10⁵

Total potential

=( 22.5 - 9 ) x 10⁵

= 13.5 x 10⁵ V

c ) In the space between the two , potential will depend upon the distance of the point from the common centre .

d ) Inside the sphere , potential will be same as that on the surface that is

13.5 x 10⁵ V.

e ) Outside the shell , potential due to both positive and negative charge will cancel each other so it will be zero.