Question

Consider an infinite slab of thickness d and uniform volume charge density ρ. This is essentially an infinite plane with a non-negligible thickness. The planar symmetry involves z to -z reflection symmetry, as well as infinite in the x-y plane. Use Gauss law to find the electric field produced outside the slab and inside the slab .

Answer 1

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

$\phi=EAcos\theta$

$\rho=\frac{q}{v}$

$\Phi=\smallint E.ds_1+\smallint E.ds_2+\int E.ds_3$

$\Phi=ES+ES+0=2ES$

$2ES=\frac{\rho S}{2\epsilon}$

$E=\frac{\rho }{2\epsilon_0 }$