GATE 2021 EE – Question 27
A 1 $\mu$C point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 $\mu$C is moved from $(0,10,0)$ to $(5,5,5)$ and subsequently to $(5,0,0)$, then the total work done is ________ mJ. (Round off to 2 decimal places).
Take $\frac{1}{4\pi\varepsilon_0}=9\times10^9$ in SI units. All coordinates are in meters.
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Show answer and explanation
Correct answer: 8.95 to 9.05
Explanation
The work depends only on the start and end distances from the charge at the origin. The start point $(0,10,0)$ is at $r=10$ m, and $(5,5,5)$ is at $8.66$ m but does not matter. The end point $(5,0,0)$ is at $r=5$ m. So $W=kQq\left(\frac1{5}-\frac1{10}\right)=9\times10^9\times10^{-6}\times10\times10^{-6}\times0.1=9\times10^{-3}$ J $=9.00$ mJ.