Question

Assertion: Two equipotential surfaces cannot cut each other.
Reason: Two equipotential surfaces are parallel to each other.
$A.$ Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
$B.$ Both assertion and Reason are true but the Reason is not the correct explanation of the Assertion
$C.$ Assertion is true but Reason is false
$D.$ Both Assertion and Reason are false statements.

Answer 1

Hint: Here we will proceed by using the meaning of equipotential surfaces, then by explaining the given assertion and reason we will get our answer.

Complete step-by-step answer:

Equipotential surface – it is defined as the surface in which the locus of all points are at the same potential is known as the equipotential surface.

Two potential surfaces cannot intersect. If they intersect, then at the point of intersection there will be two values of potential, which is not possible two. They cannot intersect each other because two different equipotential surfaces have different electric potential.

Now we know that the potential difference between any two points is zero in an equipotential surface. Also, we know that the electric field is perpendicular to the equipotential surface and their intersection shows that there are two different directions of the electric field at their intersection point which is not possible.

Therefore, the given Assertion is true.

Now the electric field is always perpendicular to the equipotential surface. If they are not perpendicular there will be two components which can cause charge to move along the surface. This means that there is some potential difference which cannot be true since equipotential surfaces, by definition, should be a surface where the potential is constant across the surface. Therefore, components of electric field intensity along the equipotential surface. It means the electric field intensity is perpendicular to the surface. Since, two equipotential surfaces can never be parallel to each other because there is no potential gradient along any direction parallel to the surface, and thus there is no electric field parallel to the surface. This means that the electric lines of force are always at right angles to the equipotential surface.

Hence,we can say that the surface is perpendicular to the electric field lines.
Therefore, Assertion is true but reason is false.

Hence, C is the correct option.

Note: Whenever we come up with this type of question related to equipotential surface. Then we will try to solve it by using various properties of the equipotential surface such as no work is done to move a charge from one point to another point on an equipotential surface. Also we can say that any surface having the same electric potential at every point is termed as an equipotential surface.