The electric dipole moment of system formed by point charge –q and uniformly charged hemisphere as shown in the figure is

Engineering

Physics

Electric Dipole

Question

$\frac{qR}{2}$

$\frac{qR}{3}$

$\frac{qR}{4}$

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$dp = \int d (dp) cosθ$

$= cosθ \int d (dp)$

$= cosθ \int d (dq) \times R$

= (R cos θ) × dθ
= R cos θ × (2π R sin θ) (Rdθ) σ

$p = \int_{0}^{π / 2} {πR}_{σ}^{2} \sin 2 θdθ$

$= {πR}_{σ}^{3} [\frac{- \cos 2 θ}{2}] = {πR}^{3} \frac{q}{2 {πR}^{2}} = q \times \frac{R}{2}$

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