Avery 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?

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

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it