Question

The textbook that the electric field due to an infinite line of charge is perpendicular to the line and has magnitude E=λ/2πϵ0rE=λ/2πϵ0r. Consider an imaginary cylinder with a radius of r = 0.155 mm and a length of l = 0.500 mm that has an infinite line of positive charge running along its axis. The charge per unit length on the line is λλlambda = 5.65 μC/mμC/m . What is the electric flux through the cylinder due to this infinite line of charge?

Answer 1

Answer:

The electric flux through the cylinder due to this infinite line of charge is $0.319209\times10^{6}\ Nm^2/C$

Explanation:

Given that,

The electric field $E=\dfrac{\lambda}{2\pi\epsilon_{0}r}$

Radius = 0.155 mm

length = 0.500 mm

Charge per unit length $\lambda=5.65\times10^{-6}\ C/m$

We need to calculate the electric flux

Using formula of electric flux

$\phi=EA\cos\theta$

Here, $\theta=90^{\circ}$

Put the value of E and A

$\phi=\dfrac{\lambda}{2\pi\epsilon_{0}r}\times(2\pi\times r\times l)$

$\phi=\dfrac{\lambda\times l}{\epsilon_{0}}$

Put the value into the formula

$\phi=\dfrac{5.65\times10^{-6}\times0.500}{8.85\times10^{-12}}$

$\phi=0.319209\times10^{6}\ Nm^2/C$

Hence, The electric flux through the cylinder due to this infinite line of charge is $0.319209\times10^{6}\ Nm^2/C$