\(dF\,\, = \,\,\frac{1}{{4\pi \,\,{ \in _0}}}\,\,\frac{{q\,dQ}}{{{x^2}}}\) પરંતુ \(dQ\,\, = \,\,(Q/L)dx\) તેથી \(dF\,\, = \,\,\frac{1}{{4\pi \,\,{ \in _0}}}\,\,\frac{{q\,Q\,dx}}{{L{x^2}}}\)
\(\therefore \,\,F\,\, = \,\,\frac{1}{{4\pi \,\,{ \in _0}}}\,\,\,\frac{{qQ}}{L}\,\,\int\limits_d^{(d\,\, + \,\,L)} {\,\,\,\frac{{dx}}{{{x^2}}}} \,\, = \,\,\frac{1}{{4\pi \,\,{ \in _0}}}\,\,\frac{{qQ}}{L}\,\,\left[ { - \frac{1}{x}} \right]_d^{(d\,\, + \,\,L)}\)
\( \Rightarrow \,\,F\,\, = \,\,\frac{1}{{4\pi \,\,{ \in _0}}}\,\,\frac{{qQ}}{L}\,\,\left[ {\frac{1}{d}\,\, - \,\,\frac{1}{{(d\,\, + \,\,L)}}} \right]\,\, = \,\,\frac{1}{{4\pi \,\,{ \in _0}}}\,\,\,\frac{{qQ}}{{d(d\, + \,\,L)}}\)
[ અત્રે $\hat{i}, \hat{j}$ અને $\hat{k}$ એ અનુક્રમે $x, y$ અને $z-$ અક્ષોની દિશામાં એકમ સદિશ છે.]