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Question

A semi circular ring of radius R as shown in figure has charge per unit length λ=λocosθ. Electric dipole moment of this ring is


A
λR2
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B
2λR2
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C
λR22
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D
32λR2
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Solution

The correct option is B 2λR2

The dipole moment by a small elemental length dl having charge dq making an angle θ with the x-axis at origin as shown in the figure, is given by :

dp=dq 2R cos θ
(considering the symmetry along y-axis)

Here,
dq=λ Rdθ

Therefore,
dp=λRdθ×2R cosθ=λ2R2cos θ dθ

p=dp=λ2R2π20cosθ dθ
( Dipole moment due to each elemental length lies in the same direction)

p=2λR2

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