A unit positive charge has to be brought from infinity to a midpoint between two charges $20 \mu \mathrm{C}$…

A unit positive charge has to be brought from infinity to a midpoint between two charges $20 \mu \mathrm{C}$ and $10 \mu \mathrm{C}$ separated by a distance of $50 \mathrm{~m}$. How much work will be required?
  1. $10.8 \times 10^4 \mathrm{~J}$
  2. $10.8 \times 10^3 \mathrm{~J}$
  3. $1.08 \times 10^6 \mathrm{~J}$
  4. $0.54 \times 10^5 \mathrm{~J}$

Solution

Given that, two charges $q_1$ and $q_2$ separated by $d=50 \mathrm{~m}, q_1=20 \mu \mathrm{C}$ and $q_2=10 \mu \mathrm{C}$
Work done in bringing $q=1 \mathrm{C}$ from infinite to point $M$ $W=q V$ where, $V$ be the electric potential at $M$ due to charges $q_1$ and $q_2$. $W=q\left[\frac{K q_1}{\left(\frac{d}{2}\right)}+\frac{K q_2}{\left(\frac{d}{2}\right)}\right]=\frac{2 K q}{d}\left[q_1+q_2\right]$ Substituting the values, we get $\begin{aligned} W & =\frac{2 \times 9 \times 10^9 \times 1}{50}[20+10] \times 10^{-6} \\ & =10.8 \times 10^3 \mathrm{~J}\end{aligned}$

Asked in: AP EAMCET 2021 (24 Aug Shift 2)

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