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Q.

A ring of radius R carries a non-uniform charge of linear density λ=λ0cosθ (see in the figure). Magnitude of the net dipole moment of the ring is
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a

πR2λ0

b

2πR2λ0

c

πR22λ0

d

4πR2λ0

answer is A.

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Detailed Solution

Charge, dq=λ0Rcosθdθ 

dipole moment=λ0cosθRdθ×2Rcosθ
=2λ0R2cos2θdθ 

The net electric dipole moment is given as,

p=rdq =02πλ0cosθRdθ

p=02πλ0R2cos2θdθ=λ0R2202π(1+cos2θ)=λ0R22θ+12sin2θ02π=λ0R2π


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A ring of radius R carries a non-uniform charge of linear density λ=λ0 cosθ (see in the figure). Magnitude of the net dipole moment of the ring is