Question

Three-point charges -q, -q and +q are situated in X-Y plane at points (0, -a), (0, 0) and (0, a) respectively. The potential at a distant point r (r>> a) in a direction making an angle $\theta$ with the X-axis is:

• A. $\frac{kq}{r}[1-\frac{2a\cos\theta}{r}]$
• B. $\frac{kq}{r}[1-\frac{2a\sin\theta}{r}]$
• C. $\frac{kq}{r}[\frac{2a\cos\theta}{r}-1]$
• D. $\frac{kq}{r}[\frac{2a\sin\theta}{r}-1]$

Answer 1

Answer: (D)

$\frac{kq}{r}[\frac{2a\sin\theta}{r}-1]$

Answer 2

The potential is obtained using multipole expansion. The monopole term gives $-\frac{kq}{r}$ and the dipole term gives $\frac{2kqa\sin\theta}{r^2}$. Their sum is $\frac{kq}{r}\left(\frac{2a\sin\theta}{r} - 1\right)$.