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

The Correct Option is B

The correct option is (B) : \(\frac{4R_q}{\pi }\hat{i}\)
\(P Q =2 R \cos \theta\)
\(d p =d q \times 2 R \cos \theta\)
\(d r =\lambda(R d \theta) \times 2 R \cos \theta\)
\(p =2 \lambda R^{2} \int\limits_{0}^{T / 2} \cos d \theta\)
\(=2 \lambda R^{2}|\sin \theta|^{\pi/2}_{0}\)
\(p =2 \lambda R^{2}\)
\(\vec{p} =2 \frac{2 q}{\pi R} \times l^{2}=\frac{4 q R}{\pi} i\)