Question

A long cylindrical volume contains a uniformly distributed charge of density $\rho$ $C{m}^{-3}$. The electric field inside the cylindrical volume at a distance $x=\frac{2{\epsilon }_0}{\rho }m$ from its axis is ______ $V{m}^{-1}$

Answer 1

Answer: 1

$\int Eds\cos 0=\frac{q}{{\epsilon }_0}$
$\Rightarrow E\cdot 2\pi xh=\frac{\rho \times \pi x^{2}h}{{\epsilon }_0}$
$\Rightarrow E=\frac{\rho x}{2{\epsilon }_0}$
$\Rightarrow E=\frac{\rho }{2{\epsilon }_0}\times \frac{2{\epsilon }_0}{\rho }=1$