Question

A very long uniform line of charge has charge per unit length 3.80 µC/m and lies along the x-axis. A second long uniform line of charge has charge -2.00 µC/m per unit length 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

(b) y = 0.600 m

Answer 1

Given that,

Charge per unit length, 1 == 3.8*10^(-6) C/m

2 = 2*10^(-6) C/m

(a)

Net electric field at y = 0.20 m

E = E1 + E2

E = (1 / r1 + 2 / r2) / 2*pi*e0

E = [(3.8*10^(-6) / 0.20) + (2*10^(-6) / 0.40 - 0.20)] / 2*3.14*8.85*10^(-12)

E = 5.21*10^5 N/C

Direction- direction of electric field due to charge lying on x-axis is towards +y-axis and the direction of electric field

due to charge at y = 0.20 m is also towards +y-axis. so direction of net electric field is towards +y - axis.

(b)

Net electric field at = 0.60 m

E = E1 - E2

E = (2 / r2 - 1 / r1) / 2*pi*e0

E = [(2*10^(-6) / 0.60 - 0.40) - (3.8*10^(-6) / 0.60)] / 2*3.14*8.85*10^(-12)

E = 6.59*10^4 N/C

Direction -

direction of electric field due to charge lying on x-axis is towards +y-axis and the direction of electric field

due to charge at y = 0.600 m is towards -y-axis. so direction of net electric field is towards -y - axis.