Answer to Question #145582 in Electricity and Magnetism for Samran Haider

Question

Devise a strategy to derive an expression of Electric Field at a point R due to an Electric
Dipole by gausss law or columbs law

Answer 1

Let the x component of the electric field strength at point P with Cartesian co-ordinates (x, y, 0)

$E_1=\frac{2p\cos\theta}{4\pi \epsilon_o r^3}$ along PD

$E_2=\frac{p\sin\theta}{4\pi \epsilon_o r^3}$ along PC

Net, electric field intensity

$E=\sqrt{E_1^2+E_2^2}$

$\Rightarrow E=\sqrt{(\frac{2p\cos\theta}{4\pi \epsilon_o r^3})^2+(\frac{p\sin\theta}{4\pi \epsilon_o r^3})^2}$

$\Rightarrow E =\frac{p}{4\pi \epsilon_o r^3} \sqrt{4\cos^2\theta +\sin^2\theta}$

$\Rightarrow E =\frac{p}{4\pi \epsilon_o r^3} \sqrt{3\cos^2\theta +1}$