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NEET PHYSICSMedium

Two parallel infinite line charges with linear charge densities +λ C/m+\lambda \text{ C/m} and −λ C/m-\lambda \text{ C/m} are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

1

Zero

2

2λπϵ0R N/C\frac{2\lambda}{\pi\epsilon_0 R} \text{ N/C}

3

λπϵ0R N/C\frac{\lambda}{\pi\epsilon_0 R} \text{ N/C}

4

λ2πϵ0R N/C\frac{\lambda}{2\pi\epsilon_0 R} \text{ N/C}

Step-by-Step Solution

The electric field due to an infinite line charge at distance rr is E=λ2πϵ0rE = \frac{\lambda}{2\pi\epsilon_0 r}. At the mid-point (distance RR from each), the fields from both charges point in the same direction. Etotal=E1+E2=λ2πϵ0R+λ2πϵ0R=2λ2πϵ0R=λπϵ0R N/CE_{total} = E_1 + E_2 = \frac{\lambda}{2\pi\epsilon_0 R} + \frac{\lambda}{2\pi\epsilon_0 R} = \frac{2\lambda}{2\pi\epsilon_0 R} = \frac{\lambda}{\pi\epsilon_0 R} \text{ N/C}.

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