Question

A semi circular ring of radius R as shown in figure has charge per unit length $\lambda ={\lambda }_{0}cos\theta$. Electric dipole moment of this ring is.

• A. $\lambda R^2$
• B. $2\lambda R^2$
• C. $\frac{\lambda R^2}{2}$
• D. $\frac{3}{2}\lambda R^2$

Answer 1

The correct option is B $2\lambda R^2$


$dp=dq2Rcos\theta$
$dq=\lambda Rd\theta$
$dp=\lambda Rd\theta \times 2Rcos\theta =\lambda 2R^{2}cos\theta d\theta$
$p=\int dp=\lambda 2R^2{\int }_0^{\frac{\pi }{2}}cos\theta d\theta =2\lambda R^2$