E$15$M$\mathrm{.}2)$ In a certain region of empty space, $$# $=,$ where $$ is a constant, but $$$

and $\%$ are constant in time.

a$)$ What is the magnitude and direction of the magnetic curl in this region in

terms of $?$

b$)$ Suppose that, in this particular case, $2$ always points in the $+$ direction and

is zero on the $=0$ plane. Find $$$ as a function of $,,,$ and $.$

c$)$ Assume that $=1000($ &

$\text{'})/.$ What is the numerical rate at which $$$ increases

or decreases with increasing $$ at a given instant of time? Do the units make

sense?