Question

The electric field and the electric potential at a point are E and V respectively. Which of the following is correct?
A. If E=0, V must be zero.
B. If V=0, E must be zero.
C. If$E\ne 0$, V cannot be zero.
D. None of these

Answer 1

Hint: You could first find the main difference in the characteristics of both the given quantities. Then you could consider each of the given conditions step by step and then provide an example for each. By using the examples you could also justify your answer. After repeating the same steps for all options, you could get the answer.

Complete Step by step solution:
In the question we are given three options regarding electric field E and electric potential V at a point that is inside a shell. We are supposed to find the correct statement among the given ones.

For, the first statement, consider the equipotential surface,
We know that the electric field is given by,
$E=-\dfrac{dV}{dx}$

For an equipotential surface with constant potential on its surface will thus have zero electric field and thereby proving the first statement wrong.

When V=0, E being a directional quantity shouldn’t be zero. This is because there can be some component that is not cancelled out while finding the net field at a point. So, the second statement is false.

Now for the third statement consider a conducting or non-conducting hollow sphere kept in a uniform electric field. For a point inside the hollow sphere the potential is found to be zero when the electric field is clearly non zero. So, C is also false.

Therefore, option D is the correct answer.

Note:
You may recall that the electric field is a vector quantity or it can be considered as a directional quantity while we know that the electric potential is scalar quantity that has only magnitude and no direction. This very fact makes it quite obvious that one of the given quantities being or not being zero doesn’t necessarily imply that the other quantity is zero.