2. (3 pts) Coil 1 has length 20cm, radius 3cm, and 100 windings per cm. Coil 2 has length 5cm, radius 1 cm, and 200 windings per cm. Coil 2 is placed completely inside Coil 1 and deep enough that any edge effects can be ignored. Take the x-axis positive to the right, both coils centered on the x-axis, and magnetic flux to the right as positive. Both coils are wound with an orientation such that a current going from left to right results in a field going from left to right inside the coils. Remember to include signs or direction (left-to-right or right-to-left) where relevant in all the questions below. a. If a current increasing by 1 mA/s in the direction from left to right passes through Coil 1, what is the rate of change of the magnetic field generated inside Coil 1? b. In the case of a, what is the resulting rate of change of the magnetic field due to Coil 1 inside Coil 2 c. What is the rate of change of total magnetic flux (remember it has many windings!) inside Coil 2 in this situation? d. What is the EMF generated in Coil 2 in this situation? e. Using these results, find the mutual induction between Coils 1 and 2. f. What is the rate of change of the magnetic flux in Coil 1 due to the change in current going through it? g. What is the EMF generated in Coil 1 in this situation? h. Using e, find the self inductance of Coil 1. h. Find the answers to all the above steps for current in the same direction decreasing by 1mA/s.