Question 881: Electrostats & Capacitance

Question

A hollow metal sphere has a radius 'r'. The potential difference between a point on its surface and at a point at a distance '3r' from its centre is 'V'. The electric intensity at the distance '3r' from the centre of the sphere will be :

Accepted Answer

Given a hollow metal sphere with a radius $r$, if it is charged, the electric field $E$ outside the sphere behaves just as if all the charge were concentrated at the center.
From the properties of spherical conductors, the potential $V$ at a distance $r$ from the center due to a point charge $Q$ is given by :
$ V(r) = \frac{kQ}{r} $
where $k$ is Coulomb's constant.
Now, let the potential at the surface of the sphere be $V_1$ and the potential at a distance $3r$ be $V_2$.
Given :
$ V_2 - V_1 = V $
$ \frac{kQ}{3r} - \frac{kQ}{r} = V $
$ \frac{kQ(1 - 3)}{3r} = V $
$ \frac{-2kQ}{3r} = V $
$ Q = \frac{-3rV}{2k} $ ... (i)
The electric field $E$ at a distance $3r$ from the center of the sphere is given by:
$ E = \frac{kQ}{(3r)^2} $
Using equation (i),
$ E = \frac{k 	imes (-3rV/2k)}{(3r)^2} $
$ E = \frac{-3rV}{2 	imes 9r^2} $
$ E = \frac{-V}{6r} $

Answer

$$\mathrm{\frac{V}{3r}}$$

Answer

3Vr

Answer

$$\mathrm{\frac{V}{r}}$$

Answer

$$\mathrm{\frac{V}{6r}}$$

Electrostats & Capacitance

A hollow metal sphere has a radius 'r'. The potential difference between a point on its surface and at a point at a distance '3r' from its centre is 'V'. The electric intensity at the distance '3r' from the centre of the sphere will be :

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