Question

Two very long line charges of uniform linear charge density +$\lambda$ and -$\lambda$ are placed along same line with the separation between the nearest ends being 2a, as shown in figure. The electric field intensity at point O is :

• A. 0
• B. $\frac{\lambda }{\pi {ϵ}_{o}a}$
• C. $\frac{\lambda }{2\pi {ϵ}_{o}a}$
• D. $\frac{\lambda }{4\pi {ϵ}_{o}a}$

Answer 1

Answer: (C)

$\frac{\lambda }{2\pi {ϵ}_{o}a}$

Force on charged particle due to positive section,
$dF=kQ\lambda dx/x^2$
$F=kQ\lambda {\int }_a^{\infty }dx/x^2=kQ\lambda /a$
The negative section creates an equal amount of force in the same direction.
Total force $=2kQ\lambda /a=Q\lambda /\left(2\pi {ϵ}_{0}a\right)$