Question

What is the electric potential at the point indicated with the dot in (Figure 1)?

figure 1

Answer 1

Potential at given point due to point charge \(=\mathrm{kQ} / \mathrm{r}\)

Potential at a point due to multiple point charges \(=\mathrm{kQ}_{1} / \mathrm{r}_{1}+\mathrm{kQ}_{2} / \mathrm{r}_{2}+\mathrm{kQ}_{3} / \mathrm{r}_{3} \ldots \ldots\).etc

From the figure

\(V=k Q / r_{1}+k Q / r_{2}+k Q / r_{3}\) as all the charges are equal

\(V=k Q\left(1 / r_{1}+1 / r_{2}+1 / r_{3}\right)\)

\(r_{1}=3 \mathrm{~cm}=0.03 \mathrm{~m}\)

\(r_{3}=4 \mathrm{~cm}=0.04 \mathrm{~m}\)

\(r_{2}=\sqrt{\left(r_{1}^{2}+r_{3}^{2}\right)}\)

\(\Rightarrow r_{2}=\sqrt{\left(0.03^{2}+0.04^{2}\right)}\)

\(\Rightarrow r_{2}=\sqrt{(0.0025)}\)

\(r_{2}=0.05 \mathrm{~m}\)

\(Q=2 n C=2^{*} 10^{-9} C\)

\(\mathrm{k}=9^{*} 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\)

\(V=9 * 10^{9} * 2 * 10^{-9}(1 / 0.03+1 / 0.05+1 / 0.04) V\)

\(\Rightarrow V=18 * 78.33 V\)

\(\therefore V=1410 \mathrm{~V},\) which is the required solution