Question

What is the total flux φ that now passes through the cylindrical surface? enter a positive number if the net flux leaves the cylinder and a negative number if the net flux enters the cylnder. what is ex(p), the value of the x-component of the electric field produced by by the line of charge at point p which is located at (x,y) = (a,0), where a = 9.2 cm?

Answer 1

Net flux through the cylindrical surface is given as

$\phi = \frac{q}{epsilon_0}$

here q = enclosed charge in the surface

so here in order to find the value of q

$q = \lambda* L$

so now we have

$\phi = \frac{\lambda * L}{\epsilon_0}$

so this is the total flux

now by Gauss's law we can find the electric field

$\int E.dA = \phi$

$\int E.dA = \frac{\lambda * L}{\epsilon_0}$

$E* 2\pi rL = \frac{\lambda * L}{epsilon_0}$

$E = \frac{\lambda}{2\pi \epsilon_0 r}$

by above expression we can find the electric field at required position