Two parallel infinite line charges having linear charge densities + and - are placed at a distance d apart in free space. If the magnitude of the net electric field midway between the two line charges is E₀ , what is the magnitude of the linear charge density ?

Step-by-step solution

The distance from each line charge to the midpoint is r = d 2 . The electric field due to the positive line charge at the midpoint is directed towards the negative line charge, with magnitude: E_+ = 2 ₀ (d/2) = ₀ d The electric field due to the negative line charge at the midpoint is also directed towards the negative line charge, with magnitude: E_- = 2 ₀ (d/2) = ₀ d Since both fields point in the same direction, the net electric field E₀ is their sum: E₀ = E_+ + E_- = ₀ d + ₀ d = 2 ₀ d Rearranging to solve for gi