For a charged spherical ball, electrostatic potential inside the ball varies with as Here, and are constants and is the distance from the center. [2023]

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Solution

Q.
For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V = 2 a r^{2} + b .$ Here, $a$ and $b$ are constants and $r$ is the distance from the center. The volume charge density inside the ball is $- λ a ε$ . The value of $λ$ is _________. ( $ε =$ permittivity of the medium) [2023]

Ans.
(12)

$E = - \frac{d V}{d r} = - 4 a r \equiv \frac{ρ r}{3 ε_{0}} (compare)$

$Result inside uniformly charged solid sphere.$

$ρ = - 12 a ε_{0}$

$λ = 12$

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