Answer
See explanation.
Work Step by Step
a. Use the expression for the self-inductance of a toroidal solenoid.
$$L=\frac{\mu_0 N^2 A}{2 \pi r}$$
$$L=\frac{(4\pi \times10^{-7}Wb/m \cdot A)(500)^2(6.25\times10^{-4}m^2)}{2 \pi (0.0400m)}=7.81\times10^{-4}H$$
b. The magnitude of the induced emf is $|\epsilon|=|L\frac{di}{dt}|$.
$$|\epsilon|=(7.81\times10^{-4}H)\frac{5.00A-2.00A}{0.00300s}=0.781V$$
c. The current is decreasing, so by Lenz’s Law, the induced emf is in the same direction as the current. It is oriented from a to b.
