Identify the correct statements in the following.
A. Electric field is in the direction of decreasing potential.
B. Electric field is in the direction of increasing potential.
C. Energy density of a capacitor is directly proportional to electric field.
D. Energy density of a capacitor is directly proportional to square of electric field.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A and D only
The field points the way the potential falls (\( E = -dV/dr \)), and the energy stored in a capacitor per unit volume is \( u = \frac{1}{2}\varepsilon_0E^{2} \).
(A) Electric field is in the direction of decreasing potential. — Correct. From \( E = -dV/dr \), the field points along the steepest fall of potential; a positive charge moves from high to low potential.
(B) Electric field is in the direction of increasing potential. — Incorrect. This is the opposite of (A).
(C) Energy density of a capacitor is directly proportional to electric field. — Incorrect. The energy density depends on \( E^{2} \), not on \( E \).
(D) Energy density of a capacitor is directly proportional to square of electric field. — Correct.
\( \displaystyle u = \frac{U}{Ad} = \frac{\frac{1}{2}CV^{2}}{Ad} = \frac{1}{2}\,\frac{\varepsilon_0A}{d}\,\frac{E^{2}d^{2}}{Ad} = \frac{1}{2}\varepsilon_0E^{2} \)
NCERT (2026-27):
Relation Between Field and Potential – “… (i) Electric field is in the direction in which the potential decreases steepest.”
Energy Stored in a Capacitor – “… If we define energy density as energy stored per unit volume of space, Eq (2.72) shows that Energy density of electric field,
\( \displaystyle u = \frac{1}{2}\varepsilon_0 E^2 \qquad (2.73) \)”