Question

At a point in space, the electric field points toward the north. In the region surrounding this point, the rate of change of potential will be zero along
$\left( {\text{A}} \right)$ North
$\left( {\text{B}} \right)$ South
$\left( {\text{C}} \right)$ North-south
$\left( {\text{D}} \right)$ East-west

Answer 1

Hint:
-The surface on which the potential is the same is known as the equipotential surface.
-On the equipotential surface no work is required to move a charge from one point to another point.
-The equipotential surface analyzes the direction of the electric field.
-Two equipotential surfaces never cross each other.

Complete step-by-step solution:
According to the question, the electric field is directed toward the north direction
Analyzing the given options:

Option $\left( {\text{A}} \right)$ says about the north direction and according to the question the electric field is along the north direction which is parallel to the equipotential surface and it does not exist so the option is not correct.

Option $\left( {\text{B}} \right)$ says about the south direction and according to the question the electric field is toward the north direction and the southward direction is opposite to the north direction which is not possible.

Option $\left( {\text{C}} \right)$ says about the north-south direction and according to the question the electric field is in the north direction and north-south which is not perpendicular to the electric field, so the option is not correct.

Option $\left( {\text{D}} \right)$ says about the east-west direction which is perpendicular to the electric field in the north direction, so this is the correct option.

Hence the correct option is $\left( {\text{D}} \right)$.

Note:
-Work done required in moving a test charge from one point to another on the equipotential surface is zero.
-Two equipotential surfaces never intersect each other.
-Equipotential surface is a concentric spherical shell.
-The direction of the potential is from high potential to low potential.