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An electric dipole of dipole moment \(\vec{p}\) is placed at the origin of the co-ordinate system along the \(z\)-axis. The amount of work required to move a charge ' \(q\) ' from the point \((a, 0,0)\) to the point \((0,0, a)\) is,
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The correct answer is:
\(\frac{p q}{4 \pi \varepsilon_0 a^2}\)
Hint : 
\(\begin{aligned} W & =q\left(V_B-V_A\right) \\ & =q\left(\frac{p}{4 \pi \epsilon_0} \cdot \frac{\cos 0}{a^2}-\frac{p \cos 90^{\circ}}{4 \pi \epsilon_0 a^2}\right) \\ & =\frac{p q}{4 \pi \varepsilon_0 a^2}\end{aligned}\)
\(\begin{aligned} W & =q\left(V_B-V_A\right) \\ & =q\left(\frac{p}{4 \pi \epsilon_0} \cdot \frac{\cos 0}{a^2}-\frac{p \cos 90^{\circ}}{4 \pi \epsilon_0 a^2}\right) \\ & =\frac{p q}{4 \pi \varepsilon_0 a^2}\end{aligned}\)
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