Question

Derive an Expression for electric potential energy of a system of two point charges in the absence of electric field.

Answer 1

Let us consider a system of two point charges Q₁ and Q₂ separated by a distance 'd' in air.

No work is done in bringing Q₁ to A, because there is no electric field.

Now the charge Q₂ is brought from \(\infty\) to the point B against the field of Q₁.

Work is done in this process.

\(W=V\times Q_2\)

Where 'V' is the potential at B due to charge Q₁ & is given by \(V=\frac{1}{4\pi\varepsilon_0}\times\frac{Q_1}{d}\)

\(\therefore W=\frac{1}{4\pi\varepsilon_0}\times\frac{Q_1}{d_1}\times Q_2\)

By def, \(W=\) electric potential energy \(=U\).

\(\therefore\,U=\frac{1}{4\pi\varepsilon_0}\times\frac{Q_1Q_2}{d}\)

Electric potential energy \(=U\).

\(d=\) distance between two charges