Question

# Derive an expression for electric field due electric dipole at a point on an equatorial line.

Solution

## Electric field at A due to the charges $$q$$ and $$-q$$ is shown in the above figure. We resolve $$E$$ into horizontal and vertical components. The vertical components $$(E \sin\theta)$$ cancel out each other and only the horizontal components survive to give net electric field at A as $$2E\cos\theta$$.Electric field at point A, $$E_A = 2E \cos\theta$$where $$E = \dfrac{q}{4\pi \epsilon_o (r^2 + a^2)}$$We get $$E_A = \dfrac{2q }{4\pi \epsilon_o (r^2 + a^2)} \cos\theta$$From figure, we have $$\cos\theta = \dfrac{a}{\sqrt{r^2 + a^2}}$$$$\therefore$$ $$E_A = \dfrac{2q a}{4\pi \epsilon_o (r^2 + a^2)^{3/2}}$$We know dipole moment $$P = 2qa$$$$\implies$$ $$E_A = \dfrac{P}{4\pi \epsilon_o (r^2 + a^2)^{3/2}}$$For $$a<<r$$, we can neglect $$a^2$$ compared to $$r^2$$.$$\implies$$ $$E_A = \dfrac{P}{4\pi \epsilon_o r^3}$$Physics

Suggest Corrections

1

Similar questions
View More

People also searched for
View More