Which of the following correctly represents the variation of electric potential $$(V)$$ of a charged spherical conductor of radius $$(R)$$ with radial distance $$(r)$$ from the centre?

For a charged spherical conductor:

• For

r<R

electric field inside conductor is zero, so potential remains constant:

$$V=\frac{1}{4\pi\varepsilon_0}\frac{Q}{R}$$

Thus graph is a horizontal line from centre to surface.

• For

r>R

potential varies as

$$V=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r}$$

so it falls as a 1/r curve.

• At

r=R

potential is continuous.

So correct graph is:

flat inside, then decreasing hyperbola outside.