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

Question

Two parallel infinite line charges +λ and -λ 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)  (2 λ/π ε 0R)  (C)  (λ/π ε 0R)  (D)  (2 λ/2 π ε 0R)

Tardigrade Admin · Accepted Answer

According to Gauss's theorem φ=(q/ε0) or E .2 π R × l=(λ/ε0) ⇒ E=(1/2 π) (λ/ε0(R / 2)) × 2 (l=1)=(2 λ/π ε0 R)

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

zero

$\frac{2 λ}{π ε _{0} R}$

$\frac{λ}{π ε _{0} R}$

$\frac{2 λ}{2 π ε _{0} R}$

According to Gauss's theorem
$ϕ = \frac{q}{ε _{0}}$ or $E .2 π R \times l = \frac{λ}{ε _{0}}$
$\Rightarrow E = \frac{1}{2 π} \frac{λ}{ε _{0} ( R /2 )} \times 2$
$(l = 1) = \frac{2 λ}{π ε _{0} R}$

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

zero

πε0​R2λ​

πε0​Rλ​

2πε0​R2λ​

According to Gauss's theorem ϕ=ε0​q​ or E.2πR×l=ε0​λ​ ⇒E=2π1​ε0​(R/2)λ​×2 (l=1)=πε0​R2λ​

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

$\frac{2 λ}{π ε _{0} R}$

$\frac{λ}{π ε _{0} R}$

$\frac{2 λ}{2 π ε _{0} R}$

According to Gauss's theorem
$ϕ = \frac{q}{ε _{0}}$ or $E .2 π R \times l = \frac{λ}{ε _{0}}$
$\Rightarrow E = \frac{1}{2 π} \frac{λ}{ε _{0} ( R /2 )} \times 2$
$(l = 1) = \frac{2 λ}{π ε _{0} R}$