Question

Electric field as a function of distance from the centre of a uniformly charged solid sphere is mathematically :

• A. a discontinuos function
• B. inversely related to distance from the centre
• C. proportional to distance from the centre
• D. none of the above

Answer 1

Answer: (A)

The variation of electric field intensity $\left(E\right)$ with distance $\left(r\right)$ from the center $\left(O\right)$ of the solid sphere is as shown:

i) Electric field intensity at the center of charged solid sphere is zero.

ii) As the distance $\left(r\right)$ from the center of solid sphere increases, electric field intensity also increases along $\left(OA\right)$ [$\because (E\propto r)$] and becomes maximum at the surface of solid sphere.

iii) As the distance $\left(r\right)$ further increases beyond the surface of sphere, electric field intensity varies inversely with $r^2$ and hten decreases.

We see from the graph that there is discontinuity at $r=R$ where electric field intensity is maximum. So, this plot is a discontinuous function.