Question

Three line charges of length L and charge density λ are placed parallel to each other, separated by a distance h, as shown in the figure below. Calculate the electric field E at point P, a distance d away from the center line charge.
Hint: Find the electric field at the point P for the center line charge and from that, use superposition for the others.

l h P d

Answer 1

Take the central line charge Now, consider a small part of line �dr� and E. field due to this part is dE = 1/4 pi epsilon_0 lambda dr/r^2 E. field due to whole line charge: E_C = integral dE = integral^d + L_d 1/4 pi epsilon_0 lambda dr/r^2 = -lambda/4 pi epsilon_0 [1/d + L - 1/d] = lambda L/ 4 pi epsilon_0(d + L)d Similarly E. field due to side line charge: E = integral d E = 1/4 pi epsilon_0 integral^squareroot (d + L)^2 + h^2_squareroot d^2 + h^2 lambad dr/r^2 = -lambda /4 pi epsilon_0 [1/squareroot (d + L)^2 + h^2 - 1/ squareroot d^2 + h^2] By looking at picture Net elec. Field at point p is E_n = 2 E cos theta + E_c = 2E times d/ squareroot d^2 + h^2 + lambda L/ 4 pi epsilon_0(d + L)d = lambda/4 pi elementof_0