Question

IF the potential at a point is maximum, then
A. the point must be occupied by a negative charge.
B. the point may be occupied by a negative charge.
C. the point must be occupied by a positive charge.
D. the point may be occupied by a positive charge.

Answer 1

The correct answer to this question lies in the formula of the electric potential of a point charge and then putting various possible values of the charge to find out the correct answer.

Complete answer:
Point charges are actually the fundamental building blocks of matter and the electric potential of a point charge is the amount of work energy needed to move a point charge from a given point to another point.

As per the question, the potential at a point is maximum. So, as we know, the formula for the electric potential of a point charge is $V=k\dfrac{q}{r}$, where $q$ is the point charge and $k$ is a constant and $r$ is the distance from the given point to the point where the charge is moved. So by putting the values of charge, we can find out the correct answer.

When the charge is positive, let the potential be ${{V}_{1}}$, the equation becomes ${{V}_{1}}=k\dfrac{(+q)}{r}$, where $q$ is the point charge and $k$ is a constant and $r$ is the distance from the given point to the point where the charge is moved. Now when the charge is negative, let the potential be ${{V}_{2}}$, therefore, the equation becomes ${{V}_{2}}=k\dfrac{(-q)}{r}$. And clearly, ${{V}_{1}}$is always greater than ${{V}_{2}}$. Hence we can conclude that if the potential is maximum, the charge must be positive.

Hence, the correct answer is option C.

Note: If in future you encounter any point where you want to know the total potential then you can use the principle of superposition of electric potential which says that we can add the potentials as numbers to get the final result.