Charges $+q$ and $-q$ are placed at points $\mathrm{A}$ and $\mathrm{B}$ respectively which are a distance $2 L$ apart, $\mathrm{C}$ is the midpoint between $\mathrm{A}$ and $\mathrm{B}$. The work done in moving a charge $+\mathrm{Q}$ along the semicircle CRD is

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Aicharya · Accepted Answer

Potential at $\mathrm{C}=\mathrm{V}_{\mathrm{C}}=0$ Potential at $\mathrm{D}=\mathrm{V}_{\mathrm{D}}$ $=k\left(\frac{-q}{L}\right)+\frac{k q}{3 L}=-\frac{2}{3} \frac{k q}{L}$ Potential difference $\mathrm{V}_{\mathrm{D}}-\mathrm{V}_{\mathrm{C}}=-\frac{2}{3} \frac{k q}{L}=\frac{1}{4 \pi \varepsilon_0}\left(-\frac{2}{3} \cdot \frac{q}{L}\right)$ $\Rightarrow$ Work done $=\mathrm{Q}\left(\mathrm{V}_{\mathrm{D}}-\mathrm{V}_{\mathrm{C}}\right)$ $=-\frac{2}{3} \times \frac{1}{4 \pi \varepsilon_0} \frac{q Q}{L}=\frac{-q Q}{6 \pi \varepsilon_0 L}$

Charges $+q$ and $-q$ are placed at points $\mathrm{A}$ and $\mathrm{B}$ respectively which are a distance…

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