Question

Find potential energy for the system of three charges of + 2 microcoulomb each placed at the vertices of an equilateral triangle of side 1 metre.

Answer 1

Given :

➳ Three point charges each of +2 uC are placed at the verticles of an equilateral triangle of side 1m.

To Find :

⟶ Electrostatic potential energy of the system.

SoluTion :

⇒ Electrostatic potential energy of two point charges each of magnitude q placed at distance r is given by

$\bigstar\:\underline{\boxed{\bf{U=\dfrac{k(q\times q)}{r}}}}$

⇒ Electrostatic potential energy is a scalar quantity so we can directly add potential energy of each pair to get net potential energy of the system.

$\leadsto\sf\:U_{net}=U_{AB}+U_{BC}+U_{AC}$

$\dag\bf\:U_{AB}=U_{BC}=U_{AC}=U$

$\leadsto\sf\:U_{net}=3U$

$\leadsto\sf\:U_{net}=3\times \dfrac{k(q\times q)}{r}$

$\leadsto\sf\:U_{net}=3\times \dfrac{9\times 10^9\times (2\times 10^{-6})^2}{1}$

$\leadsto\underline{\boxed{\bf{U_{net}=0.108\:J}}}$