Question

The equation of an equipotential line in an electric field is $y=2x$, then the electric field strenght vector at $(1,2)$ may be:

• A. $4\hat{i}+3\hat{j}$
• B. $4\hat{i}+8\hat{j}$
• C. $8\hat{i}+4\hat{j}$
• D. $-8\hat{i}+4\hat{j}$

Answer 1

The correct option is D $-8\hat{i}+4\hat{j}$

In this case, equipotential surface is a straight line having slope $2$,
We know that at any point on equipotential surface, electric field should be perpendicular to the equipotential surface.
$(1,2)$ lies on our equipotential surface therefore field at this point should be perpendicular to the equipotential surface.
Hence our electric field will in the direction of line having slope $(-1/2)$
our our field should make an angle $\arctan (-1/2)$ with x- axis
which is true only in option (D) therefore option (D) is correct