# Charge density and potential in a semiconductor

 HW Helper P: 5,003 For 4(a), write Ohm's law in the form $\vec{J}=\sigma\vec{E}$. What do you get when you take the divergence of each side of the equation? For 4(b), $J_i=\delta_{ij}(\sigma_{ij}E_j)$ and $\vec{\nabla}\cdot\vec{J}=\partial_iJ_i$ For 5, Use gauss' law to get an expression for the fields in n and p type materials in terms of the two unknown charge densities $\sigma_{-}$ and $\sigma_{+}$ assume that the charge densities are constant and integrate the fields over the thickness of each slab to find an expression for the potential difference. Then set that equal to 0.3V and assume that the overall charge on the junction is zero, so that $\sigma_{+}=-\sigma_{-}$ and solve for the charge densities.