In a region of constant potential,

The correct answer is Option (4) → The electric field is zero in the region.

The electric field is the negative gradient of potential: it measures how fast the potential changes with distance.

    \( \displaystyle E = -\frac{dV}{dr} \)

If \( V \) is the same everywhere in the region, \( dV/dr = 0 \) in every direction, so \( E = 0 \) throughout the region.

Option (4) The electric field is zero in the region. — Correct. No change of potential means no electric field.

NCERT (2026-27):
Relation Between Field and Potential – “… The work done in this process is |E|δl. This work equals the potential difference V_A – V_B. Thus,

    \( \displaystyle |\mathbf{E}|\,\delta l = V - (V + \delta V) = -\,\delta V \quad \text{i.e.,} \quad |\mathbf{E}| = -\frac{\delta V}{\delta l} \qquad (2.20) \)

… 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. (ii) Its magnitude is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at the point.”