JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Electrostatics

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.

Answer: 12

Solution

The field inside follows from

E = - \frac{d V}{d r} = - 4 a r

. For a uniformly charged sphere the field at radius

r

E = \frac{ρ r}{3 ε}

. Matching the two,

- 4 a r = \frac{ρ r}{3 ε}

, so

ρ = - 12 a ε

. Comparing with the given

ρ = - λa ε

, the value of

λ

12

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Integer answer