Two charges $q_{1}$ and $q_{2}$ are placed 30 cm apart, as shown in the figure. A third charge $q_{3}$ is moved along the arc of a circle of radius $40 \mathrm{~cm}$ from $C$ to $D$. The change in the potential energy of the system is $\frac{q_{3}}{4 \pi \varepsilon_{0}} k$, where…

Question

Two charges $q_{1}$ and $q_{2}$ are placed 30 cm apart, as shown in the figure. A third charge $q_{3}$ is moved along the arc of a circle of radius $40 \mathrm{~cm}$ from $C$ to $D$. The change in the potential energy of the system is $\frac{q_{3}}{4 \pi \varepsilon_{0}} k$, where $\mathrm{k}$ is (take $\mathrm{q}_{2}=1 \mathrm{C}$)

Aicharya · Accepted Answer

Change in potential energy $(\Delta U)=U_{f}-U_{i}$ $\Rightarrow \Delta U=\frac{1}{4 \pi \varepsilon_{0}}\left[\left(\frac{q_{1} q_{3}}{0.4}+\frac{q_{2} q_{3}}{0.1}\right)-\left(\frac{q_{1} q_{3}}{0.4}+\frac{q_{2} q_{3}}{0.5}\right)\right]$ $\Rightarrow \Delta U=\frac{1}{4 \pi \varepsilon_{0}}\left[8 q_{2} q_{3}\right]=\frac{q_{3}}{4 \pi \varepsilon_{0}}\left(8 q_{2}\right)$ $\therefore k=8 q_{2}=8$

Two charges \(q_{1}\) and \(q_{2}\) are placed 30 cm apart, as shown in the figure. A third charge \(q_{3}\)…

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