Question

Two charges of equal magnitude 'q' but 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 the point P is given by $(r\gg 2a)$ (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 $V=\frac{1}{4\pi {ϵ}_0}.\frac{pcos\theta }{r^2}$