Spread the love

Total Electrostatic Energy Of A System

Total electrostatic energy of a system :- Total Electrostatic Energy of a System is the sum of the self-energy of individual charged conductors and the interaction energy between different charges or conductors.

Total Electrostatic Energy (U) = Sum of all self-energies (U_self) + Sum of all interaction energies (U_interaction)

Let us consider some examples :

(1). Two charged conducting spheres

Let us consider two spherical conductors with radii, and , carrying charges and respectively. Let the distance between their centers be

U = U_self + U_interaction

$\displaystyle U=\frac{kQ_{1}^{2}}{2{{R}_{1}}}+\frac{kQ_{2}^{2}}{2{{R}_{2}}}+\frac{k{{Q}_{1}}{{Q}_{2}}}{r}$

(2). Two charged non-conducting spheres

Let us consider two non-conducting spheres with radii, and , carrying charges and respectively. Let the distance between their centers be

U = U_self + U_interaction

$\displaystyle U=\frac{3kQ_{1}^{2}}{5{{R}_{1}}}+\frac{3kQ_{2}^{2}}{5{{R}_{2}}}+\frac{k{{Q}_{1}}{{Q}_{2}}}{r}$

(3). A system of two charged concentric shells

Consider a system of two concentric spherical shells with radii and , uniformly charged with charges and , respectively.

U = U_{self energy of inner shell} + U_{self energy of outer shell} + U_interaction

$\displaystyle U=\frac{kQ_{1}^{2}}{2{{R}_{1}}}+\frac{kQ_{2}^{2}}{2{{R}_{2}}}+\frac{k{{Q}_{1}}{{Q}_{2}}}{{{R}_{2}}}$

Total Electrostatic Energy Of A System

Like this: