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 \,\varepsilon _{0}R} $
• C. $ \frac{\lambda}{\pi \,\varepsilon _{0}R} $
• D. $ \frac{2 \lambda}{2 \pi \,\varepsilon _{0}R} $

Answer 1

Answer: (B)

According to Gauss's theorem
$\phi=\frac{q}{\varepsilon_{0}}$ or $E .2 \pi R \times l=\frac{\lambda}{\varepsilon_{0}}$
$\Rightarrow E=\frac{1}{2 \pi} \frac{\lambda}{\varepsilon_{0}(R / 2)} \times 2$
$(l=1)=\frac{2 \lambda}{\pi \varepsilon_{0} R}$