Question

The linear charge density on the circumference of a ring of radius ‘R’ is $\lambda ={\lambda }_{0}sin\theta$ where $\theta$ is defined as shown in figure. Find the magnitude of electric dipole moment (in coulomb.m) of the right if
${\lambda }_0=\frac{1}{\pi }SIunitandR=1m.$

• A. 1
• B. 2
• C. 0.5

Answer 1

The correct option is A 1

$P_{res}=\int \left(dp\right)sin\theta =\int \left(dq2R\right)sin\theta =2R\int \left(\lambda dI\right)sin\theta =2R{\lambda }_0\int \left(sin\theta dI\right)sin\theta =2R{\lambda }_0\int \left(si{n}^2\theta Rd\theta \right)2R^2{\lambda }_0{\int }_0^{\pi }si{n}^2\theta d\theta =R_0^{\lambda }\pi =1$