Question

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. Find the electric field at a point P inside the cylindrical volume at a distance x from its axis (figure 30-E5)

Answer 1

Charge on the cylinder of radius x

$=\rho \pi x^{2}h$

We know,

$\oint E.ds=\frac{q}{{\in }_0}$

$E.2\pi xh=\frac{\pi \rho x^{2}h}{{\in }_0}$

or $E=\frac{\rho x}{2{\in }_0}$