Question

Two parallel infinite line charges $+\lambda$. and $-\lambda$, are placed with a separation distance $R$ in free space. The net electric field exactly mid-way between the two line charges is

• A. zero
• B. $\frac{2\lambda }{\pi {\epsilon }_{0}R}$
• C. $\frac{\lambda }{\pi {\epsilon }_{0}R}$
• D. $\frac{\lambda }{2\pi {\epsilon }_{0}R}$

Answer 1

Answer: (B)

Electric field at point $P$ due to line charge distribution $+\lambda$,
$E_{+\lambda }=\frac{\lambda }{2\pi {\epsilon }_0\left(\frac{R}{2}\right)}$ away from $+\lambda$
Electric field at point $P$ due to line charge distribution $-\lambda$,
$E_{-\lambda }=\frac{\lambda }{2\pi {\epsilon }_0\left(\frac{R}{2}\right)}$ towards $-\lambda$
$E_{+\lambda }$ and $E_{-\lambda }$ have same direction,
$\therefore E_{net}=E_{+\lambda }+E_{-\lambda }=2\left(\frac{\lambda }{2\pi {\epsilon }_0\left(\frac{R}{2}\right)}\right)$
$=\frac{2\lambda }{\pi {\epsilon }_{0}R}$