Question

Which of the following statements is not true?

• A. Equipotential surfaces for a uniform electric field are parallel and equidistant from each other.
• B. Electric field is always perpendicular to an equipotential surface.
• C. Work done to move a charge on an equipotential surface is not zero.
• D. Equipotential surfaces are the surfaces where the potential is constant.

Hint:

On an equipotential surface, the electric potential is constant, so no work is done in moving a charge along it.

Answer 1

The Correct Option is C

Equipotential surfaces are surfaces where the electric potential is constant. The key points are: 1. Equipotential surfaces for a uniform electric field are parallel and equidistant from each other: This is true for a uniform electric field. In such a field, the potential difference between two adjacent equipotential surfaces is constant, so they are parallel and equidistant. 2. Electric field is always perpendicular to an equipotential surface: This is true. The electric field is always normal (perpendicular) to the equipotential surfaces, as any component of the electric field along the surface would do work on a charged particle, which contradicts the definition of an equipotential. 3. Work done to move a charge on an equipotential surface is not zero: This is false. Since the electric potential is constant on an equipotential surface, there is no change in potential energy when a charge moves along the surface. Therefore, no work is done. 4. Equipotential surfaces are the surfaces where the potential is constant: This is true. By definition, equipotential surfaces are those where the potential is constant across the entire surface. Thus, the statement "Work done to move a charge on an equipotential surface is not zero" is false. Therefore, the correct answer is: \[ \text{(3) Work done to move a charge on an equipotential surface is not zero.} \]