Question

Find the electric field intensity at an axial position of an electric dipole.

Answer 1

$$\begin{gathered} Letusconsideranelectricdipoleoflength2lhavingdipolemomentp=2ql. \\ LettherebeanaxialpointPatdis\tan cerfromthemidpointofthedipole. \\ SoelectricfieldatthispointPisgivenby \\ E=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q}{{\left(r+l\right)}^2}-\frac{q}{{\left(r-l\right)}^2}\right] \\ orE=\frac{q}{4\pi {\epsilon }_0}\left[\frac{4rl}{{\left(r^2-l^2\right)}^2}\right]=\frac{1}{4\pi {\epsilon }_0}\left[\frac{2\times 2ql\times r}{{\left(r^2-l^2\right)}^2}\right] \\ orE=\frac{1}{4\pi {\epsilon }_0}\left[\frac{2pr}{{\left(r^2-l^2\right)}^2}\right] \\ Thisistheelectricfieldatanaxialpointdis\tan cerfromthemidpoint \\ oftheelectricdipole. \\ Ifr>>lthenE=\frac{1}{4\pi {\epsilon }_0}\times \frac{2p}{r^3} \end{gathered}$$