Identify the correct statements among the following:
(A) The electrostatic potential is necessarily zero at a point where the electric field strength is zero.
(B) The electrostatic potential at a point can be zero where electric field is not zero.
(C) In an electric field, an electron moves from higher to lower potential region.
(D) In an electric field, an electron moves from lower to higher potential region.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
The electric field depends on how fast the potential changes, \( E = -\frac{dV}{dr} \), not on the value of V, and it points from higher to lower potential.
(A) The electrostatic potential is necessarily zero at a point where the electric field strength is zero. — Incorrect. At the midpoint between two equal positive charges the two fields cancel, so E = 0, but the potentials add: \( V = 2 \times \frac{kq}{r} \ne 0 \).
(B) The electrostatic potential at a point can be zero where electric field is not zero. — Correct. At the midpoint of an electric dipole the potentials of +q and −q cancel, so V = 0, but both fields point from +q towards −q and add, so E is not zero.
(C) In an electric field, an electron moves from higher to lower potential region. — Incorrect. The force on an electron, \( \vec{F} = -e\vec{E} \), is opposite to the field, so a free electron moves towards higher potential.
(D) In an electric field, an electron moves from lower to higher potential region. — Correct. For the same reason, an electron released in the field moves opposite to \( \vec{E} \), from lower to higher potential.