Question

Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p . If P is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $\theta$ with the axis of the dipole, then the potential at P is given by (r >> 2a) (Where p = 2qa)

• A. $V=\frac{pcos\theta }{4\pi {ϵ}_0{r}^2}$
• B. $V=\frac{pcos\theta }{4\pi {ϵ}_{0}r}$
• C. $V=\frac{psin\theta }{4\pi {ϵ}_{0}r}$
• D. $V=\frac{pcos\theta }{2\pi {ϵ}_0{r}^2}$

Answer 1

The correct option is A $V=\frac{pcos\theta }{4\pi {ϵ}_0{r}^2}$

For the given situation, diagram can be drawn as follows
As shown in figure component of dipole moment along the line OP will be $p^{{}^{\prime }}=pcos\theta$. Hence electric potential at point P will be $V=\frac{1}{4\pi {ϵ}_0}.\frac{pcos\theta }{r^2}$