Question

An infinitely long line charge of uniform linear charge density λ = -2.10 µC/m lies parallel to the y axis at x = -3.00 m. A point charge of 2.40 µC is located at x = 2.00 m, y = 3.00 m. Find the electric field at x = 3.00 m, y = 2.50 m.

Answer 1

GIVEN INFINITELY Long liner of charge
charge density, lamdba = 2.1 uC/m
parallel to y axis at x = -3 m

q = 2.4 uC is at x = 2 m, y = 3 m

at x = 3, y = 2.5 m
electric field due to line charge = E1
E1 = 2k*lambda/x i ( towards +x axis)

similiarly
E2 = kq(i - 0.5j)/(1^2 + 0.5^2)^3/2

hence
E1 = 12572 i V/m
E2 = 15421.355i - 7710.6779 j V/m

Enet = E1 + E2 = 27993.3558 i - 7710.6779j V/m

|E| = 29035.8831775 V/m
direction = arctan(Ey/Ex) = -15.4 deg CCW to +x axis