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.

Solution:

As we know that electric potential is a scalar quantity

Since the potential due to all charges is a scalar sum of potential due to all charges on the equilateral triangle.

so, we have

$V = \frac{{k{q_1}}}{r} + \frac{{k{q_2}}}{r} + \frac{{k{q_3}}}{{r'}}$

r=5 cm

r’ = $5\sqrt 3 $

Now Using the above Formula

$V = {\rm{ }}\frac{{(9 \times {{10}^9})(1.8 \times {{10}^{ - 6}})}}{{0.05}} + \frac{{(9 \times {{10}^9})(1.8 \times {{10}^{ - 6}})}}{{0.05}} + \frac{{(9 \times {{10}^9})(1.8 \times {{10}^{ - 6}})}}{{0.05\sqrt 3 }}$

$V{\rm{ =  324000(1 + 1 + }}\frac{1}{{\sqrt 3 }})$

V = 8.35 * 10 ⁵ V/m