CBSE 2025 · Region 7 · Set 2 · Q28 · 3 marks
Two point charges of $\displaystyle -5 \mu \mathrm{C}$ and $\displaystyle 2 \mu \mathrm{C}$ are located in free space at ( $\displaystyle -4 \mathrm{~cm}, 0$ ) and ( $\displaystyle 6 \mathrm{~cm}, 0$ ) respectively.(a)Calculate the amount of work done to separate the two charges at infinite distance.(b)If this system of charges was initially kept in an electric field $\displaystyle \mathrm{E}=\frac{\mathrm{A}}{\mathrm{r}^{2}}$, where $\displaystyle \mathrm{A}=8 \times 10^{4} \mathrm{NC}^{-1} \mathrm{~m}^{2}$, calculate the electrostatic potential energy of the system.
Two point charges of $\displaystyle -5 \mu \mathrm{C}$ and $\displaystyle 2 \mu \mathrm{C}$ are located in free space at ( $\displaystyle -4 \mathrm{~cm}, 0$ ) and ( $\displaystyle 6 \mathrm{~cm}, 0$ ) respectively.
(a)
Calculate the amount of work done to separate the two charges at infinite distance.
(b)
If this system of charges was initially kept in an electric field $\displaystyle \mathrm{E}=\frac{\mathrm{A}}{\mathrm{r}^{2}}$, where $\displaystyle \mathrm{A}=8 \times 10^{4} \mathrm{NC}^{-1} \mathrm{~m}^{2}$, calculate the electrostatic potential energy of the system.
Marking-scheme solution
(a) \(\displaystyle \mathrm{U}=\frac{\mathrm{kq}_{1} \mathrm{q}_{2}}{\mathrm{r}}\)
\[\begin{aligned}
& =\frac{9 \times 10^{9} \times\left(-5 \times 10^{-6}\right) \times\left(2 \times 10^{-6}\right)}{10 \times 10^{-2}} \\
& =-0.9 \mathrm{~J}
\end{aligned}
\]
\[\mathrm{W}=\mathrm{U}(\text { infinity })-\mathrm{U}(\mathrm{r})=0.9 \mathrm{~J}
\]
(b) \(\displaystyle \mathrm{E}=\frac{-\mathrm{dV}}{\mathrm{dr}}\)
\[\begin{aligned}
& d V=\frac{-\mathrm{A}}{\mathrm{r}^{2}} d \mathrm{r} \\
& V=\frac{\mathrm{A}}{\mathrm{r}}
\end{aligned}
\]
\[\mathrm{U}=\mathrm{q}_{1} V_{1}+\mathrm{q}_{2} V_{2}+\frac{k \mathrm{q}_{1} \mathrm{q}_{2}}{\mathrm{r}}
\]
\[\begin{aligned}
= & \left(-5 \times 10^{-6}\right)\left(\frac{8 \times 10^{4}}{4 \times 10^{-2}}\right)+\left(2 \times 10^{-6}\right)\left(\frac{8 \times 10^{4}}{6 \times 10^{-2}}\right)-0.9 \\
& =-10+2.67-0.9 \\
& =-8.24 \mathrm{~J}
\end{aligned}
\]
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CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.