Question

A long cylindrical volume contains a uniformly distributed charge of density $\rho$ $Cm ^{-3}$. The electric field inside the cylindrical volume at a distance $x =\frac{2 \varepsilon_0}{\rho} m$ from its axis is ______ $Vm ^{-1}$

Answer 1

$ \int E d s \cos 0=\frac{ q }{\varepsilon_0}$
$ \Rightarrow E \cdot 2 \pi xh =\frac{\rho \times \pi x ^2 h }{\varepsilon_0} $
$ \Rightarrow E =\frac{\rho x }{2 \varepsilon_0} $
$ \Rightarrow E=\frac{\rho}{2 \varepsilon_0} \times \frac{2 \varepsilon_0}{\rho}=1$