Which of the following is the correct relation between electric intensity E and electric potential V:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( E=\displaystyle\frac{-dV}{dr} \)
The electric field is the negative gradient of the potential: it equals the rate at which the potential falls per unit distance, and it points in the direction of decreasing potential. The potential is the quantity that is differentiated, and the minus sign is essential.
\( \displaystyle E = -\frac{dV}{dr} \)
Among the four relations, only Option (3) has this form, with E obtained from V and carrying the minus sign. Options (1) and (2) give V as a derivative of E, which is the wrong way round, and Option (4) lacks the minus sign.
Note: The same question was also asked in CUET (UG) 2023 on 23-06-2023 (Slot 1).
NCERT (2026-27):
Relation Between Field and Potential – “… This work equals the potential difference VA–VB. Thus,
\( \displaystyle |\mathbf{E}|\,\delta l = V - (V + \delta V) = -\delta V \)
i.e.,
\( \displaystyle |\mathbf{E}| = -\frac{\delta V}{\delta l} \qquad (2.20) \)”
Relation Between Field and Potential – “… We thus arrive at two important conclusions concerning the relation between electric field and potential: (i) Electric field is in the direction in which the potential decreases steepest.”