An infinite line charge of linear density λ = 0.30 μC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m. The x component of the electric field at the point P on the x axis at x = 3.0 m is approximately
A) 1.8 kN/C B) 4.2 kN/C C) 0.96 kN/C D) 5.2 kN/c E) 0.64 mN/C

Question

An infinite line charge of linear density λ = 0.30 μC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m. The x component of the electric field at the point P on the x axis at x = 3.0 m is approximately 
	A)  1.8 kN/C     B)  4.2 kN/C     C)  0.96 kN/C     D)  5.2 kN/c     E)  0.64 mN/C

jamesj · Answer

Start as ever with a diagram.

Then clearly the electric field in total at the point p = (3,0,0) is the sum of the electric field of the two sources.  The point source is easy to deal with; just make sure you calculate the x-component.

The line source has an electric field given by
$$ E = \frac{\lambda}{2\pi r \epsilon_0} $$
where r is the radial distance; and this field points also in the direction of the line.

So, calculate those two, their x-components, and add them up.