Question

The dipole moment of the given charge distribution is:

• A. $-\frac{4R_q}{\pi } \hat{i}$
• B. $ \frac{4R_q}{\pi }\hat{i}$
• C. $-\frac{2R_q}{\pi }\hat{i}$
• D. $\frac{2R_q}{\pi }\hat{i}$

Answer 1

Answer: (B)

$P Q =2 R \cos \theta $
$ d p =d q \times 2 R \cos \theta$
$ d r =\lambda(R d \theta) \times 2 R \cos \theta $
$p =2 \lambda R^{2} \int\limits_{0}^{T / 2} \cos d \theta $
$=2 \lambda R^{2}|\sin \theta|^{\pi/2}_{0}$
$ p =2 \lambda R^{2} $
$ \vec{p} =2 \frac{2 q}{\pi R} \times l^{2}=\frac{4 q R}{\pi} i $