Task $7$: Electric Flux and Gauss's Law

Objective: To illustrate the concept of "flux" and to avoid performing the integral in

Gauss's Law for Electricity.

A cylindrical Gaussian surface $($length $=0\mathrm{.}80m,$ diameter $=0\mathrm{.}20m)$ is drawn in an

area of a non$-$uniform electric field, directed at all points in the $+x$ direction $($i$.$e$.,$

horizontal to the right$).$ The field varies with $x,$ but does not vary with respect to $y$

or z$.$ The side of the Gaussian surface is aligned

along the $x$ direction, and the two ends of the

surface are normal to the $x-$direction. The

electric fields $E_1$ and $E_2,$ at the ends of the

surface, have magnitudes of $3\mathrm{.}0{10}^3\frac{N}{C}$ and

$7\mathrm{.}0{10}^3\frac{N}{C}.$

a$.$ Calculate the electric flux through each surface of the cylinder $($hint: there are

three$).$ Be careful about units and significant figures!

b$.$ Calculate the net electric flux through the cylinder. Be careful about signs!

c$.$ Why was the length of the cylinder irrelevant to your calculations?