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

Answer:

The magnitude of the net electric field is $6.57\times10^{5}\ N/C$

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

$E=E_{1}+E_{2}$

$E=\dfrac{1}{2\pi\epsilon_{0}}(\dfrac{\lambda}{r}+\dfrac{\lambda'}{r'})$

Put the value into the formula

$E=\dfrac{1}{2\pi\times8.85\times10^{-12}}(\dfrac{4.54\times10^{-6}}{0.204}+\dfrac{2.58\times10^{-6}}{0.384-0.204})$

$E=6.57\times10^{5}\ N/C$

Hence, The magnitude of the net electric field is $6.57\times10^{5}\ N/C$