Question

A thin non-conducting ring of radius a has
a linear charge density 1. = 1., sin. A
uniform electric field Ei-Ej is present in
the region. Torque acting on the ring is​

Answer 1

Total dipole moment = πa²λo

Explanation:

Given: A thin non-conducting ring of radius a hasa linear charge density λ = λo sin  θ. A uniform electric field Ei-Ej is present in the region.

Find: Torque acting on the ring.

Solution:

Dipole moment of the charge pair at P and Q.

dp = [ (λo Sinθ) a dθ] (2a Sinθ)

Total dipole moment = 2λoa² ∫Sin²θ.dθ (range is -π/2 to π/2)

   = πa²λo