Question

Charge is distributed uniformly throughout the volume of an infinitely long solid Cylinder of radius R what is the electric field when r < Select one : O a . Zero O b . E = / 2 € d . E = pr / 2 € O e . E = / 2 €

Answer 1

Let us consider the Gaussian surface that is in the form of a cylinder having a radius of r and a length of A which is
`$\text{coaxial with the charged cylinder}$`.

The charged enclosed by the cylinder is given by,

`$q=\rho V$` (here, V =
`$\pi r^2l$` is the volume of the cylinder)

`$=\pi r^2lp$`

If
`$\rho$` is positive, then the electric field lines moves in the radial outward direction and is normal to Gaussian surface which is distributed uniformly.

Therefore, total flux through Gaussian cylinder is :

`$\phi=EA_(cyl)$`

`$=E(2\pi rl)$`

Now using Gauss' law, we get

`$2\pi \epsilon_0rlE = \pi r^2lp$`

or
`$E=(\rho r)/(2 \epsilon_0)$`

Therefore, the electric field is
`$E=(\rho r)/(2 \epsilon_0)$`

Hence, option (d) is correct.