$3.(31$ points$)$ A circular loop of wire with radius $\backslash ($ r$=0\mathrm{.}0470\backslash$mathrm$\{$~m$\}\backslash )$ and resistance $\backslash ($ R$=0\mathrm{.}170\backslash$Omega $\backslash )$ is in a region of a spatially uniform magnetic field, as shown in the following figure. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of $8\mathrm{.}12$ T and the magnitude is increasing at a rate of $\backslash (0\mathrm{.}698\backslash$mathrm$\{$~T$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($a$)(10$ points$)$ Is the induced current I in the loop clockwise or counterclockwise?

$($b$)(10$ points$)$ What is the magnitude of the current I? Hint: USE

OHM'S LAW AS DISCUSSED IN CHAPTER $25$ AND $26.$

$($c$)(8$ points$)$ What is the rate at which electrical energy is being dissipated by the resistance of the loop? Hint: See chapter $25.$

$($d$)(3$ points$)$ Did the initial value $8\mathrm{.}12$ T of the magnetic field affect your answers? Hint: No$.$ Explain.