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A thin non-conducting ring of radius R has a linear charge density $λ = λ_{0} \cos θ$ , where $θ$ is measured as shown. The total electric dipole moment of the charge distribution is

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$R^{2} λ_{0}$

$2 {πR}^{2} λ_{0}$

$\frac{{πR}^{2} λ_{0}}{2}$

${πR}^{2} λ_{0}$

answer is D.

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Detailed Solution

Dipole moment of the charge pair at P and Q.

$dp = [(λ_{0} \cos θ) Rdθ] (2 Rcos θ)$

Total dipole moment

$= 2 λ_{0} R^{2} \int_{- π / 2}^{π / 2} \cos^{2} θdθ = {πR}^{2} λ_{0}$

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