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Two parallel infinite line charges with linear charge densities +λ C/m and -λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?
- zero
- 2λ / πε₀ R N/C
- λ / πε₀ R N/C
- λ / 2πε₀ R N/C
Correct answer: 2λ / πε₀ R N/C
Solution
The electric field due to each line charge at the midpoint is equal in magnitude but opposite in direction. Since the charges are of opposite signs, the fields add up. The magnitude of the electric field due to one line charge at a distance R is λ / (2πε₀R). Adding the contributions from both charges gives the total field as 2λ / (πε₀R).
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