Question

Two equal charges, 2.0 × 10⁻⁷ C each, are held fixed at a separation of 20 cm. A third charge of equal magnitude is placed midway between the two charges. It is now moved to a point 20 cm from both the charges. How much work is done by the electric field during the process?

Answer 1

Let the third charge be moved from point A to point B.


Magnitude of the charges, q = 2.0 × 10⁻⁷ C
Distance of both the charges from point A, r = 10 cm =0.1 m
Distance of both the charges from point B, r' = 20 cm =0.2 m
Potential at A, $V_A=2\times \frac{1}{4\mathrm{\pi }{\epsilon }_0}\frac{q}{r}$
Potential at B, $V_B=2\times \frac{1}{4\mathrm{\pi }{\epsilon }_0}\frac{q}{r\text{'}}$
Work done, $W=q\left(V_B-V_A\right)$
$$\begin{gathered} \Rightarrow W=2\times {10}^{-7}\left[\frac{2\times 2\times {10}^{-7}}{4{\mathrm{\pi \epsilon }}_0}\left(\frac{1}{0.1}-\frac{1}{0.2}\right)\right] \\ \Rightarrow W=3.6\times {10}^{-3}\mathrm{J} \end{gathered}$$