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 constant 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 medium.

Question

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 constant 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 medium.

Aicharya · Accepted Answer

As we know, E = - d V d r = - 4 a r Now, electric field inside the charged sphere is given by E = &#961; r 3 &#949; . Comparing both, we get &#961; = - 12 a &#949; . Therefore, &#955; = 12 .

For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2 a r 2 + b .…

Solution