Question

The electrostatic potential inside a charged spherical ball is given by `Phi = ar^2 + b`, where r is the distance from the centre a, and b are constants. Then the charge density inside the ball is ______.

विकल्प

• -6aε₀r

• -24πaε₀

• -6aε₀

• -24πaε₀r

Answer 1

The electrostatic potential inside a charged spherical ball is given by `Phi = ar^2 + b`, where r is the distance from the centre a, and b are constants. Then the charge density inside the ball is -6aε₀.

Explanation:

Electric field, E = `-(dPhi)/(dt) = (-d)/(dt)(ar^2 + b) = -2ar`

By Gauss's theorem, E(4πr²) = q/ε₀

⇒ q = -8πε₀ar²

∴ Charge density, `rho = (dq)/(dV) = (dq)/(dr) xx (dr)/(dV) = (-24piε_0ar^2) xx 1/(4pir^2)`

⇒ `rho = -6ε_0a`