Question

In an electric dipole, what is the locus of zero potential?

Answer 1

An electric dipole is a couple of charges having equal magnitude and opposite charge separated by a distance. The easiest example would be two charges of equal magnitude and opposite charge separated by a distance. A locus is the set of all points satisfying some condition. For instance, the locus of a point equidistant from one point makes a circle. Now that we have the definition of a dipole and a locus, let us attempt the question.

Complete answer:
Here we can see that the given condition is of zero electric potential. Let us think about where the value of electric potential is zero. The value of electric potential at infinity is zero, the electric potential in a straight line through the center of the dipole is also zero due to the charges. In the first case of electric potential being zero is at infinity, it is not considered. We consider the second case. Hence the locus points will be in a straight line passing through the center of the separation of the dipole.

In conclusion, the locus points will be a line passing through the center of the electric dipole.

Note: We discard the case of the electric potential being zero at infinity because it is harder to imagine and the concept of locus defines the existence of curves like the parabola, circle, ellipse etc. The condition for loci (plural of locus) is that there must be a condition with respect to both the charges. If the condition of infinity is considered, we do not arrive at the required conclusion and it will not be following the condition.