First slide

Equipotential surfaces

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

Moderate

A

$4 \hat{i} + 3 \hat{j}$
B

$4 \hat{i} + 8 \hat{j}$
C

$8 \hat{i} + 4 \hat{j}$
D

$- 8 \hat{i} + 4 \hat{j}$

Solution

Field lines will be perpendicular to equipotential surface . Slope of equipotential surface $m_{1} = 2$ and slope of electric field lines is $m_{2}$ .
therefore $m_{1} \times m_{2} = - 1 \Rightarrow m_{2} = - \frac{1}{2} .$

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