$\backslash$#$5-$ Magnetic Induction: A circular loop of wire of resistance $0\mathrm{.}2$ ohms encloses an area of $0\mathrm{.}5$ square meters and lies flat on a wooden table as shown below. A magnetic field that varies with time $\backslash ($ t $\backslash )$ as shown below is perpendicular to the table. A positive value of $\backslash ($ B $\backslash )$ represents a field directed up from the surface of the table; a negative value represents a field directed into the tabletop.

a$.$ Calculate the value of the magnetic flux through the loop at time $\backslash ($ t$=3\backslash )$ seconds.

b$.$ Calculate the magnitude of the emf induced in the loop during the time interval $\backslash (\backslash$mathrm$\{$t$\}=0\backslash )$ to $2$ seconds.

c$.$ On the axes below, graph the current I through the coil as a function of time $\backslash ($ t $\backslash ),$ and put appropriate numbers on the vertical scale. Use the convention that positive values of I represent counterclockwise current as viewed from above.

d$.$ Draw a diagram of the magnetic field generated by the loop when it has current flowing through is in the

clockwise direction, as viewed from above.

e$.$ If you were to place a bar magnet above the loop $($with the current described in part d$.),$ describe bow the

magnet would respond to the field of the loop, both in terms of translational and rotational motion. You should

have a diagram as a part of your answer here.