Question

Do two equipotential surfaces intersect each other? Answer with reason.

Hint:

Remember that equipotential surfaces represent regions of constant electric potential, and the electric field is always perpendicular to these surfaces. Two equipotential surfaces cannot intersect because this would imply that a point could have two different potentials, which is impossible.

Answer 1

An equipotential surface is a surface on which the electric potential is constant at every point. It is defined such that no work is done in moving a charge along the surface because the electric potential difference between any two points on the surface is zero. The electric field is always perpendicular to the equipotential surface.
To answer the question, we need to consider the implications if two equipotential surfaces were to intersect.
1. Electric Potential at a Point:
- The electric potential at a point in space is a scalar quantity, meaning that at any given point, the potential has a single value.
- If two equipotential surfaces were to intersect, it would imply that a point would have two different potential values (since each surface corresponds to a different potential). This is a contradiction because a point cannot have two distinct potential values at the same time.
2. Electric Field Direction:
- The electric field is always perpendicular to the equipotential surface. If two equipotential surfaces were to intersect, the direction of the electric field would have to be ambiguous at the point of intersection because there would be two perpendicular directions corresponding to the two surfaces. This would violate the definition of the electric field.
3. Conclusion:
- Therefore, two equipotential surfaces can never intersect. If they did, it would imply a violation of the uniqueness of electric potential at any given point in space, and it would lead to an undefined situation for the electric field.
Thus, two equipotential surfaces cannot intersect.