$5.(40$ points$)$ CH$.29,$ SECTION $29\mathrm{.}7.$ DISPLACEMENT CURRENT: A parallel$-$plate, air$-$filled capacitor is being charged as in Fig. $29\mathrm{.}23$ SHOWN BELOW. The circular plates have a radius of $8\mathrm{.}00$ cm $,$ and at a particular instant the conduction current in the wires is $1\mathrm{.}200$ A $.$

$($a$)(10$ points$)$ What is the total displacement current density in the air space between the plates?

$($b$)(10$ points$)$ What is the rate at which the electric field between the plates is changing? $($Find $\backslash (\backslash$mathrm$\{$dE$\}/\backslash$mathrm$\{$dt$\}\backslash ).)$

$($c$)(10$ points$)$ What is the induced magnetic field magnitude $\backslash ($ B $\backslash )$ between the plates at a distance of $4\mathrm{.}00$ cm from the axis?

$($d$)(10$ points$)$ What is the induced magnetic field magnitude $\backslash ($ B $\backslash )$ between the plates at a distance of $2\mathrm{.}00$ cm from the axis?

Figure $29\mathrm{.}23$

A capacitor being charged by a current $\backslash ($ i $\backslash )$ ches a displacement current equal to $\backslash ($ i$=\backslash )$ between the plates, with

plates.