Question

Find the potential due the dipole when the angle subtended by the two charges at the point P is perpendicular.

• A. Unity
• B. 10
• C. Infinite
• D. 0

Answer 1

Answer: (D)

0

Answer 2

The condition "the angle subtended by the two charges at the point P is perpendicular" implies that the point P lies on a circle whose diameter is the line segment connecting the two charges. For a dipole with charges at $(-a,0)$ and $(a,0)$, this circle has its center at the origin and a radius of $a$. The equation of this locus is $x^2+y^2=a^2$.

The electric potential due to a dipole at a point $(x,y)$ is given by $V = \frac{1}{4\pi\epsilon_0} \frac{2qx}{a^2}$, where $2aq$ is the dipole moment and $a$ is half the separation between charges.

For points on the equatorial plane (y-axis, where $x=0$), the potential is zero. The points $(0,a)$ and $(0,-a)$ lie on both the equatorial plane and the circle $x^2+y^2=a^2$. At these points, the angle subtended by the charges is indeed $90^\circ$, and the potential is $0$.