Electrostatics Question 11

Question 11 - 29 January - Shift 2

For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V=2 ar^{2}+b$.

Here, $a$ and $b$ are constant and $r$ is the distance from the center. The volume charge density inside the ball is $-\lambda a \varepsilon$. The value of $\lambda$ is

$\varepsilon=$ permittivity of medium.

Show Answer

Answer: (12)

Solution:

Formula: Electric Potential

$E=-\frac{dV}{dr}=-4 ar \equiv \frac{\rho r}{3 \varepsilon_0}$ (compare)

Result inside uniformly charged solid sphere

$\rho=-12 a \varepsilon_0$

$\lambda=12$