Question

An insulated sphere of radius R has a volume charge density $\rho$ . The variation of its potential with respect to the distance from the centre is best represented by

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The variation of electric potential due to a uniformly charged sphere (one with volume charge density)
with distance from the centre is given by
$V=\{\begin{array}{cc}\frac{kQ}{2R}& (3-\frac{r^2}{R^2})forr<R\\ \frac{kQ}{r}& forr>R\end{array}$
If you don’t know this and are wondering “How on earth am I supposed to know that?” then I strongly recommend you to go through the derivation video for ‘Electric potential due to uniformly charged spherical distribution’ Now we have for $r<R,V=\frac{KQ}{2R}$ $(3-\frac{r^2}{R^2})$ this is an equation of an inverted parabola (a quadratic in r) if we put r=0, we get $V=\frac{3KQ}{r}$ we now know that the graph doesn’t start from (0,0) but $(0,\frac{3KQ}{2R})$ option (b) and (c) is obviously incorrect.
and when r>R, we have $V=\frac{KQ}{r}$ is a hyperbolic curve. The graph will shift to hyperbola at r=R. Option (d) is a single curve. Option (a) is correct.