Answer: What do you need help with?
Explanation:
Both are at the side of the spectrum that has the lower frequency
In series with the circuit, so for it pass the current to be mensured.
Letter A
If you notice any mistake in my english, please let me know, because i am not native.
Answer:
Part a)

Part B)

Part C)

Explanation:
Part a)
Magnetic field due to a long ideal solenoid is given by

n = number of turns per unit length



now we know that magnetic field due to solenoid is


Now magnetic flux due to this magnetic field is given by




Part B)
Now for mutual inductance we know that




now we have


Part C)
As we know that induced EMF is given as



Here
- Acceleration and initial velocities are constant.
According to first equation of kinematics.




- Time was t at velocity v
- Time will be 4t at velocity 4v