A loop of wire with radius $r=0\mathrm{.}055m$ is placed in a region of uniform magnetic field with magnitude $B.$ As shown in the figure, the field direction is perpendicular to the plane of the loop. The magnitude of the magnetic field changes at a constant rate from $B_1=0\mathrm{.}85T$ to $B_2=8\mathrm{.}5T$ in time $t=5\mathrm{.}5s.$ The resistance of the wire is $R=4.$ Part a: enter an expression for the magnitude of the magnetic flux through the loop using symbols $.$ Your expression must be valid at all times described in the problem statement

Part $($b$)$

Enter an expression for the change in the magnitude of the magnetic flux through the loop using the symbols in the palette below.

Part $($c$)$

Calculate the numerical value, in tesla squared meters, of the change in the magnitude of the flux.

Part $($d$)$

Enter an expression for the magnitude of the induced emf in the loop using the symbols in the palette.

Part $($e$)$

Calculate, in volts, the numerical value of the magnitude of the emf.

Part $($t$)$

Enter an expression for the magnitude of the current induced in the loop using the symbols in the palette.

Part $($E$)$

Calculate the numerical value, in amperes, of the magnitude of the induced current.

Part $($h$)$

If you are looking down at the loop from above, so that the magnetic field is directed towards you, what is the direction of the induced current?