2023-02-20

A point charge ${q}_{1}=-5.8\mu C$ is held stationary at the origin. A second charge $q2=+4.3\mu C$ moves from the point (0.26 m,0,0) to (0.38 m,0,0). Find the workdone by the electric force on ${q}_{2}$.
A. −0.272 J
B. +0.272 J
C. −0.381 J
D. +0.381 J

mandyllau34fy

Given,
${q}_{1}=-5.8\mu C,{q}_{2}=+4.3\mu C$
${r}_{i}=0.26m,{r}_{f}=0.38m$
Workdone by the electrostatic force $W={U}_{i}-{U}_{f}$
$\because \Delta U=\frac{{q}_{1}{q}_{2}}{4\pi {\epsilon }_{0}}\left(\frac{1}{{r}_{f}}-\frac{1}{{r}_{i}}\right)$
We can write that,
$W=\frac{{q}_{1}{q}_{2}}{4\pi {\epsilon }_{0}}\left(\frac{1}{{r}_{i}}-\frac{1}{{r}_{f}}\right)$
$W=\frac{\left(-5.8×10-6\right)\left(4.3×10-6\right)\left(9×109\right)\left(0.38-0.26\right)}{0.38×0.26}$
$⇒W=-0.272J$
Therefore, option (a) is the correct answer.

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