Question

Three charges are at the corners of an equilateral triangle with sides 9m. What is the potential energy of these charges.( q1 = q2 = 4×10^(-4)C and q3 = -3×10^(-4)C and K=9×10⁹ )

Answer 1

Potential Energy of $q_1$ with respect to $q_2$

$U_{12}=K\dfrac{q_1q_2}{r}=9\times 10^{9}\times \dfrac{4\times 10^{-4}\times 4\times 10^{-4}}{9}=160J$

Potential Energy of $q_2$ with respect to $q_3$

$U_{23}=K\dfrac{q_2q_3}{r}=9\times 10^{9}\times \dfrac{4\times 10^{-4}\times -3\times 10^{-4}}{9}=-120J$

Potential Energy of $q_3$ with respect to $q_1$

$U_{13}=K\dfrac{q_1q_3}{r}=9\times 10^{9}\times \dfrac{4\times 10^{-4}\times -3\times 10^{-4}}{9}=-120J$

Net energy $U=U_{12}+U_{23}+U_{13}=160-120-120=-80J$