Problem 109 - A Complete Resource Book in Physics for JEE Main

Question

Choose the correct statements from the following: (A) If the electric field is zero at a point, the electric potential must also be zero at that point. (B) If electric potential is constant in a given region of space, the electric field must be zero in that region. (C) Two different equipotential surfaces can never intersect. (D) Electrons move from a region of lower potential to a region of higher potential.

Step-by-Step Solution

Answer

The correct statements are (B) "If electric potential is constant in a given region of space, the electric field must be zero in that region" and (C) "Two different equipotential surfaces can never intersect."

Step 1: Statement A

"If the electric field is zero at a point, the electric potential must also be zero at that point." This statement is not always true. The electric potential at a point depends on the reference point from where we measure the potential. If the electric field is zero at a point, it means that there is no net force acting on a charged particle at that point, but it does not imply that the electric potential is zero.

Step 2: Statement B

"If electric potential is constant in a given region of space, the electric field must be zero in that region." This statement is true. The electric field at a point is the negative gradient of the electric potential with respect to position. If the electric potential is constant within a given region of space, that means the gradient of the potential is zero, which implies that the electric field is zero.

Step 3: Statement C

"Two different equipotential surfaces can never intersect." This statement is also true. Equipotential surfaces are surfaces on which all points have the same electric potential. If two equipotential surfaces were to intersect, it would mean that there would be some points on the intersection with different electric potentials. This contradicts the definition of equipotential surfaces, and hence, two different equipotential surfaces cannot intersect.

Step 4: Statement D

"Electrons move from a region of lower potential to a region of higher potential." This statement is false. Electrons, being negatively charged particles, tend to move from regions of higher potential to regions of lower potential. Hence, the correct statement should be "Electrons move from a region of higher potential to a region of lower potential." Therefore, the correct statements are (B) and (C).