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 -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 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 -λ a ε. The value of λ is ε= permittivity of medium. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

E =-( dV / dr )=-4 ar ≡ (ρ r /3 ε0) (compare) Result inside uniformly charged solid sphere. ρ=-12 a ε0 λ=12

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 constant and $r$ is the distance from the center. The volume charge density inside the ball is $- λa ε$ . The value of $λ$ is ____ $ε =$ permittivity of medium.

$E = - \frac{d V}{d r} = - 4 a r \equiv \frac{ρ r}{3 ε _{0}}$ (compare)
Result inside uniformly charged solid sphere.
$ρ = - 12 a ε_{0}$
$λ = 12$

Q. For a charged spherical ball, electrostatic potential inside the ball varies with r as V=2ar2+b. Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is −λaε. The value of λ is ____ ε= permittivity of medium.

E=−drdV​=−4ar≡3ε0​ρr​ (compare) Result inside uniformly charged solid sphere. ρ=−12aε0​ λ=12

$E = - \frac{d V}{d r} = - 4 a r \equiv \frac{ρ r}{3 ε _{0}}$ (compare)
Result inside uniformly charged solid sphere.
$ρ = - 12 a ε_{0}$
$λ = 12$