Question

A very long uniform line of charge has charge per unit length 4.54 μC/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.58 μC/m and is parallel to the x-axis at y1 = 0.384 m .

What is the magnitude of the net electric field at point y2 = 0.204 m on the y-axis?

Answer 1

The magnitude of the net electric field is
`6.57*10^(5)\ N/C`

Step-by-step explanation:

Given that,

Charge density
`\lambda = 4.54\ \mu C/m`

Charge density
`\lambda' = -2.58\ \mu C/m`

Distance
`y_(1)= 0.384\ m`

Distance
`y_(2)= 0.204\ m`

We need to calculate the magnitude of the net electric field

Using formula of electric field

`E=E_(1)+E_(2)`

`E=(1)/(2\pi\epsilon_(0))((\lambda)/(r)+(\lambda')/(r'))`

Put the value into the formula

`E=(1)/(2\pi*8.85*10^(-12))((4.54*10^(-6))/(0.204)+(2.58*10^(-6))/(0.384-0.204))`

`E=6.57*10^(5)\ N/C`

Hence, The magnitude of the net electric field is
`6.57*10^(5)\ N/C`