First slide

Electrostatic potential

Question

A field of 100 Vm^–1 is directed at 30^o to positive x-axis. Find (V_A–V_B) if OA = 2 m and OB = 4 m

Moderate

A

$100 (\sqrt{3} - 2) V$
B

$+ 100 (2 + \sqrt{3}) V$
C

$100 (2 - \sqrt{3}) V$
D

$200 (2 + \sqrt{3}) V$

Solution

$\begin{array}{rcl} \vec{E} & = & 100 \cos 30^{o} \hat{i} + 100 \sin 30^{o} \hat{j} \\ = & 100 \frac{\sqrt{3}}{2} \hat{i} + 100 \frac{1}{2} \hat{j}; \\ \vec{dl} & = & 2 \hat{i} + 4 \hat{j}; \\ dV & = & - (\vec{E} . \vec{dl}) \\ = & - (100 x \frac{\sqrt{3}}{2} x 2 + 100 x \frac{1}{2} x 4) = - 100 (\sqrt{3} + 2) V \\ V_{B} - V_{A} & = & - 100 (\sqrt{3} + 2) V ∴ V_{A} - V_{B} = 100 (\sqrt{3} + 2) V \end{array}$

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