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

Question #145582
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
1
Expert's answer
2020-11-23T10:16:09-0500

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


E1=2pcosθ4πϵor3E_1=\frac{2p\cos\theta}{4\pi \epsilon_o r^3} along PD


E2=psinθ4πϵor3E_2=\frac{p\sin\theta}{4\pi \epsilon_o r^3} along PC

Net, electric field intensity

E=E12+E22E=\sqrt{E_1^2+E_2^2}

E=(2pcosθ4πϵor3)2+(psinθ4πϵor3)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}

E=p4πϵor34cos2θ+sin2θ\Rightarrow E =\frac{p}{4\pi \epsilon_o r^3} \sqrt{4\cos^2\theta +\sin^2\theta}

E=p4πϵor33cos2θ+1\Rightarrow E =\frac{p}{4\pi \epsilon_o r^3} \sqrt{3\cos^2\theta +1}


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