First slide

Electrostatic potential

Question

Equipotential surfaces are shown in figure. Then the electric field strength will be

Moderate

A

100 vm^-1 along X-axis
B

100 vm^-1 along Y-axis
C

200 vm^-1 at an angle 120° with X-axis
D

50 vm^-1 at an angle 120° with X-axis

Solution

$Using dV = - \vec{E} \cdot d \vec{r} \Rightarrow ΔV = - E . Δrcosθ \Rightarrow E = \frac{- ΔV}{Δrcosθ} \Rightarrow E = \frac{- (20 - 10)}{10 \times 10^{- 2} \cos 120 °} = \frac{- 10}{10 \times 10^{- 2} (- \sin 30 °)} = \frac{- 10^{2}}{- 1 / 2} = 200 V / m$
Direction of E be perpendicular to the equipotential surface i.e., at 120° with x-axis.

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