Question

Three equal charges 1.8*10^(-6) C each are located at the corners of an equilateral triangle ABC of each side 10 cm. Calculate the electric potential due to these charges at the midpoint of AB.

Answer 1

The potential of a charge e at a distance d is given by

$$\phi = \frac{ke}{d}$$

with k = 8.988 10⁹ V m / C.

If the length of a side of the triangle is l, the corresponding distances are 0.5l, 0.5l for the charges in points A, B and

$$\frac{\sqrt{3}}{2} l$$

for the charge in point C due to known expression for the altitude.

Thus

$$\phi = \phi_A + \phi_B + \phi_C = \frac{2ke}{\,\,l\,\,} + \frac{2ke}{l} + \frac{2ke}{\sqrt{3}l}$$

$$\phi = \frac{ke}{l} (4+\frac{2}{\sqrt{3}}) \approx 8.3\cdot 10^{5} V$$