The potential difference $\left(V_A-V_B\right)$ in the arrangement shown in the figure is $(q=1 \mu \mathrm{C}, x=2 \mathrm{~cm}, y=3 \mathrm{~cm})$

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Aicharya · Accepted Answer

An arrangement is shown in the figure below,

Here, potential at a point $A$, $ \begin{gathered} V_A=V_{A^{+q}}+V_{A^{-q}} \\ =\frac{9 \times 10^9 \times 10^{-6}}{2 \times 10^{-2}}-\frac{9 \times 10^9 \times 10^{-6}}{5 \times 10^{-2}}=9 \times 10^5\left[\frac{1}{2}-\frac{1}{5}\right] \end{gathered} $ Similarly, potential at a point $B$, $ V_B=V_{B^{+q}}+V_{B^{-q}}=9 \times 10^5\left[\frac{1}{5}-\frac{1}{2}\right] $ Hence, $V_A-V_B=9 \times 10^5\left[\frac{1}{2}-\frac{1}{5}-\frac{1}{5}+\frac{1}{2}\right]$ $ \Rightarrow \quad V_A-V_B=5.4 \times 10^5 \mathrm{~V} $ Hence, the correct option is (a)

The potential difference $\left(V_A-V_B\right)$ in the arrangement shown in the figure is $(q=1 \mu…

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