Problem $1$: Surface charge density $(5$ pts$.)$

A square sheet has a side$-$length $L$ as shown at right. A charge $+q$ is uniformly

distributed over the sheet.

A$.$ What is the surface charge density $($charge per unit area$)$ on the sheet, $?$

B$.$ Draw a Gaussian surface which would allow you to find the electric field

at point $P,$ to the right of the sheet as shown. Label the cross$-$sectional

area of the surface as $A.$

C$.$ For your Gaussian surface, find:

The enclosed charge $q_{\text{e}\text{n}\text{c}}$ within the sheet.

The net flux through the surface, in terms of the electric field $E$ at point $P.$

D$.$ Use your expressions above with Gauss' law to find $E$ in terms of the given variables.