Question

The electric potential at a point on the equatorial line of an electric dipole is?
(A) Directly proportional to the distance
(B) Inversely proportional to the distance
(C) inversely proportional to the square of the distance
(D) None of the above

Answer 1

Hint:Electric potential can be defined as a region in the space where some work is needed to be done to move an electric charge. The existence of electric potential has its origin in the electric field. The electric field is defined as the negative gradient of electric potential. An electric dipole is defined as the combination of two charges having the same magnitude but opposite polarity separated by some distance. There are broadly two points: the axial axis and the equatorial axis.

Complete step by step answer:
We know that the electric potential due to an electric dipole at a given point is given by \[\dfrac{KP\cos \theta }{{{r}^{2}}-{{a}^{2}}{{\cos }^{2}}\theta }\] where 2a is the distance between the two charges and r is the distance of the point where the potential is to be find from the dipole. $\theta $is the angle that is made by the line where potential is to be found with the dipole axis.Now if the potential is to be found at the equatorial axis. Equatorial axis is that axis, which is perpendicular to the dipole and thus the angle $\theta ={{90}^{0}}$. We know $\cos 90=0$and thus the potential becomes zero.

So, the correct option is D.

Note: Electric potential is a scalar quantity and it is assumed to be zero at the infinity. If we want to move a charge from one point to another and if the electric potential is same at both the points work done will be zero because no work is required to be done to move a charge on an equipotential surface.The electric potential is related to electric field and electric field is defined as the negative gradient of electric potential.