Question

What is the shape of an equipotential surface for a uniform electric field?

Answer 1

Hint: In this question, we need to determine the shape of an equipotential surface in a uniform electric field. For this, we will use the properties of the equipotential surface and the electric field.

Complete step by step solution:
We know an equipotential surface is a surface which has equal potential at every point in a surface
V =constant, if we consider two points on an equal potential surface then the potential difference between those two points will be equal to zero,
 $dV = 0$
Also, we know that work done in moving a charge from one point to another is directly proportional to the potential difference between that two-point hence we can say in an equipotential surface work done is zero because the potential difference between two points is zero
$dW = 0$
We also know that the direction of the equipotential surface is always perpendicular to the uniform electric field lines. Now let us consider a uniform electric field line moving along the positive x-axis direction, this can be shown as

Now we know that the equipotential surface is always perpendicular to the uniform electric fields and since the electric field is moving along the positive x-axis direction, hence we can say that the equipotential surface will be in the y-z direction. This can be shown as

Note: It is interesting to note here that the direction of the equipotential surface is always perpendicular to the uniform electric field lines. Moreover, the electric field lines never intersect each other at any point during its travel