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 -2.32 μC/m and is parallel to the x-axis at y1 = 0.414 m .

Part A

What is the magnitude of the net electric field at point y2 = 0.214 mon the y-axis?

Part B

What is the magnitude of the net electric field at point y3 = 0.616 mon the y-axis?

Answer 1

A)

A line of charge having charge per unit length = p₁ = 4.8 μC/m lies along the x-axis.

A second line of charge has charge per unit length = p₂= -2.32 μC/m and is parallel to the x-axis at y₁= 0.414m .

point y₂= 0.214 m on the y-axis

y₂ is between the lines.As one is +ive and the other is - ve, the field will be added up,it will be towards second -ve line

E =2k[ p₁/r₁ + p₂/r₂ ]

E =2*9*10⁹[ 4.8 *10^-6/0.214 +2.32 *10^-6 /0.214 ]

E = 5.53*10⁵ N/C

The direction of the net electric field at point y₂= 0.214 m on the y-axis is along +y-axis

B) point y₃= 0.616 m on the y-axis

At y₃, the field are in opposite direction, the field due to positive is less than field due to negative

Total field will be difference of two fields

E = 2k[ p₁/r₁ - p₂/r₂ ]

E = 18*10³[ 4.8 /0.616 - 2.32 /0.202]

E = -19.89*10⁴ N/C

The direction of the net electric field at point y₃ = 0.616 m on the y-axis is -y-axis