Question

The equation of an equipotential line in an electric field is $y=2x$, then the electric field strength 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 $-8\hat{i}+4\hat{j}$

Now equation of equipotential surface is $y=2x$
Now electric field along the euipotential surface should be zero
therefore angle made by equipotential surface with x-axis is $ta{n}^{-1}\left(2\right)$
Now since net electric field should be perpendicular to the equipotential surface
therefore for any electric field which makes an angle $ta{n}^{-1}(-1/2)$ with x-axis can be the electric field at point $(1,2)$ which is true only for option (D)

because for two perpendicular line, product of their slope should be equal to -1 i.e., $m_1\times m_2=-1$