Question

What is the electric potential at the point indicated with the dot in the figure?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Use the properties of equilateral triangle,

\(\begin{aligned} r &=\frac{a}{\sqrt{3}} \\ &=\frac{3}{\sqrt{3}} \\ &=\sqrt{3} \mathrm{~cm} \end{aligned}\)

\(=\sqrt{3} \times 10^{-2} \mathrm{~m}\)

The potential at given point is, \(V=\frac{k q_{1}}{r}+\frac{k q_{2}}{r}+\frac{k q_{3}}{r}\)

\(=\frac{k}{r}\left(q_{1}+q_{2}+q_{3}\right)\)

\(=\frac{9 \times 10^{9}}{\sqrt{3} \times 10^{-2}}\left(1 \times 10^{-9}-2 \times 10^{-9}-2 \times 10^{-9}\right)\)

\(=\frac{9 \times 10^{9} \times 10^{-9} \times(-3)}{\sqrt{3} \times 10^{-2}}\)

\(=\frac{-27}{\sqrt{3}} \times 10^{2}\)

\(=-1558 \mathrm{~V}\)

Thus, the electric potential at the point indicated (rounding off to two significant figures) is \(-1600 \mathrm{~V}\).