Which of the following statements are correct?
A. Electric field lines are always perpendicular to equipotential lines.
B. A zero electric field inside a conducting sphere does not mean that the potential gradient is also zero
C. The resultant of two electric fields is determined by vector addition of the two field strengths
D. If the field lines get closer together at any place, it means that the field strength is decreasing
E. The resultant potential at a point is just the sum of the individual potentials.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A, C and E only
The electric field and the potential are linked by \( E = -dV/dr \): the field is the negative potential gradient.
(A) Electric field lines are always perpendicular to equipotential lines. — Correct. No work is done in moving a charge along an equipotential, so the field can have no component along it.
(B) A zero electric field inside a conducting sphere does not mean that the potential gradient is also zero — Incorrect. Since \( E = -dV/dr \), a zero field means a zero potential gradient. The potential inside the sphere is constant.
(C) The resultant of two electric fields is determined by vector addition of the two field strengths — Correct. By the superposition principle, fields due to different charges add as vectors.
(D) If the field lines get closer together at any place, it means that the field strength is decreasing — Incorrect. The density of field lines measures the field strength, so lines crowding together mean a stronger field, not a weaker one.
(E) The resultant potential at a point is just the sum of the individual potentials. — Correct. Potential is a scalar, so the potentials due to different charges add algebraically.
NCERT (2026-27):
Summary – “… The electric field E at a point is perpendicular to the equipotential surface through the point.”
Physical Significance of Electric Field – “… By the superposition principle, the electric field E at r due to the system of charges is (as shown in Fig. 1.9)
\( \displaystyle \mathbf{E}(\mathbf{r}) = \mathbf{E}_1(\mathbf{r}) + \mathbf{E}_2(\mathbf{r}) + \dots + \mathbf{E}_n(\mathbf{r}) \)”
Potential Due to a System of Charges – “… By the superposition principle, the potential V at P due to the total charge configuration is the algebraic sum of the potentials due to the individual charges
\( \displaystyle V = V_1 + V_2 + \dots + V_n \qquad (2.17) \)”