Question

A very long uniform line of charge has charge per unit length 4.80 μC/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.40 μC/m and is parallel to the x-axis at y = 0.400 m. What is the net electric field (magnitude and direction) at the following points on the y-axis: (a) y = 0.200 m and (b) y = 0.600 m?

Answer 1

Answer:

a) 647 kN/C

b) -71.9 kN/C

Explanation:

Using Gauss law relating electric flux to the charge contained inside a surface we arrive at this equation for the electric field around a infinite charged line:

E = ρ / (2 * π * r * e0)

The electric field on the XY plane will be the sum of the electric fields caused by both lines:

E(y) = ρ1 / (2 * π * (y - Y1) * e0) + ρ2 / (2 * π * (y - Y2) * e0)

With

Y1 = 0 (the position in Y where the first line is)

Y2 = 0.4

e0 = 8.85*10^-12

ρ1 and ρ2 are the charges per unit of length of the lines

At point y = 0.2

E(0.2) = 4.8*10^-6 / (2 * π * (0.2) * 8.85*10^-12) -2.4*10^-6 / (2 * π * (0.2 - 0.4) * e8.85*10^-12) = 647 kN/C

At point y = 0.6

E(0.6) = 4.8*10^-6 / (2 * π * (0.6) * 8.85*10^-12) -2.4*10^-6 / (2 * π * (0.2 - 0.6) * e8.85*10^-12) = -71.9 kN/C