Question

A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its centre (1) increases as r increases for r < R (2) decreases as r increases for $0<r<\infty$ (3) decreases as r increases for $R<r<\infty$ (4) is discontinuous at $r=R$

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (D)

Inside the sphere $E=\frac{1}{4\pi {\epsilon }_0}.\frac{Q}{R^3}r$ $E\propto r$ for $r\le R$ i.e., E at centre = 0 as $r=0$ and E at surface
$=\frac{1}{4\pi {\epsilon }_0}.\frac{Q}{R^2}$ as $r=R$
Outside the sphere $E=\frac{1}{4\pi {\epsilon }_0}.\frac{Q}{r^2}$ for $r\ge R$ or $E\propto \frac{1}{r^2}$
Thus, variation of electric field (E) with distance (r) from the centre will be shown