Question:

The dipole moment of the given charge distribution is:

Updated On: Jan 30, 2025
  • 4Rqπi^-\frac{4R_q}{\pi } \hat{i}
  • 4Rqπi^\frac{4R_q}{\pi }\hat{i}
  • 2Rqπi^-\frac{2R_q}{\pi }\hat{i}
  • 2Rqπi^\frac{2R_q}{\pi }\hat{i}
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The Correct Option is B

Solution and Explanation

The correct option is (B) : 4Rqπi^\frac{4R_q}{\pi }\hat{i}
PQ=2RcosθP Q =2 R \cos \theta
dp=dq×2Rcosθd p =d q \times 2 R \cos \theta
dr=λ(Rdθ)×2Rcosθd r =\lambda(R d \theta) \times 2 R \cos \theta
p=2λR20T/2cosdθp =2 \lambda R^{2} \int\limits_{0}^{T / 2} \cos d \theta
=2λR2sinθ0π/2=2 \lambda R^{2}|\sin \theta|^{\pi/2}_{0}
p=2λR2p =2 \lambda R^{2}
p=22qπR×l2=4qRπi\vec{p} =2 \frac{2 q}{\pi R} \times l^{2}=\frac{4 q R}{\pi} i
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Concepts Used:

Electric Dipole

An electric dipole is a pair of equal and opposite point charges -q and q, separated by a distance of 2a. The direction from q to -q is said to be the direction in space.

p=q×2a

where,

p denotes the electric dipole moment, pointing from the negative charge to the positive charge.

Force Applied on Electric Dipole