Question

An infinite line charge of uniform linear charge density lambda = -3.1 mu or micro CC/m lies parallel to the y axis at x = 0 m. A point charge of 0.6 mu or micro CC is located at x = 2.0 m, y = 3.0 m. Find the x component of the electric field at x = 3.0 m, y = 2.5 m. Answer in kN/C

Answer 1

so for the given question, the diagram can be made as above

given Q = 0.6 e-6 C at (2,3)

let P (3,2.5) be the point where we need to find the electric field

so from the figure we can find the angle

Now consider a Gaussian cylinder of radius r = 3m ( the x coordinate of P)

then we have E1 * 2* pi * L = lambda * L / epsilon

so we get E1 =

now E2 due to the point charge is given by

E2 =

from figure R =

E2 =

now total electric field E = E1+E2= -18.583+4.32 = -14.263 kN/C

it will be in -ve x direction towards the infinte line of charge