Question

A uniformly charged linear rod is placed as shown in the figure. Find the electric field intensity at point P. Given that charge density is $\lambda$ C/m.

• A. $\frac{\lambda (b-a)}{4\pi {ϵ}_{\circ }ab}$
• B. $\frac{\lambda (b^2-a^2)}{4\pi {ϵ}_{\circ }ab}$
• C. $\frac{\lambda }{2\pi {ϵ}_{\circ }}\frac{(b-a)}{ab}$
• D. $\frac{\lambda }{4\pi {ϵ}_{\circ }}ln\left(\frac{b}{a}\right)$

Answer 1

The correct option is A

$\frac{\lambda (b-a)}{4\pi {ϵ}_{\circ }ab}$

$dE=\frac{k\left(\lambda dx\right)}{x^2}E=\int dE=k\lambda {[-\frac{1}{x}]}_a^b=k\lambda [\frac{1}{a}-\frac{1}{b}]=\frac{\lambda (b-a)}{4\pi {ϵ}_{\circ }ab}$