# Worksheet: Mutual Inductance of Conducting Loops

In this worksheet, we will practice calculating the mutual inductance of systems involving multiple solenoids or conducting loops.

**Q1: **

A coil of 40 turns is wrapped around a long solenoid of
cross-sectional area m^{2}. The solenoid is 0.50 m long and has 500 turns.

What is the mutual inductance of this system?

- A H
- B H
- C H
- D H
- E

The outer coil is replaced by a coil of 40 turns whose radius is three times that of the solenoid. What is the mutual inductance of this configuration?

- A H
- B H
- C
- D
- E H

**Q2: **

An emf of V is induced in a coil while the current in a nearby coil is decreasing at a rate of 2.7 A/s. What is the mutual inductance of the two coils?

- A H
- B H
- C H
- D H
- E H

**Q3: **

A toroidal coil has a mean radius of 16 cm and a
cross-sectional area of 0.25 cm^{2}; it is wound uniformly
with turns. A second toroidal coil of 750 turns is
wound uniformly over the first coil. Ignoring the variation
of the magnetic field within a toroid, determine the mutual
inductance of the two coils.

- A H
- B H
- C H
- D H
- E

**Q4: **

When the current in one coil changes at a rate of 3.1 A/s, an emf of V is induced in a second nearby coil. What is the mutual inductance of the two coils?

- A H
- B H
- C H
- D H
- E H

**Q5: **

Two coils close to each other have a mutual inductance of 36 mH. If the current in one coil decays according to , where and , what is the emf induced in the second coil immediately after the current starts to decay at ?

- A V
- B V
- C V
- D V
- E V

**Q6: **

A 500 turn solenoid is 0.60 m long and 5.5 cm in diameter. Inside the solenoid, a small single-turn circular coil is fixed in place with its face perpendicular to the long axis of the solenoid. What is the mutual inductance of this system?

- A H
- B H
- C H
- D H
- E H

**Q7: **

A solenoid of turns has length m and radius , and a second, smaller solenoid of turns has length and radius . The smaller solenoid is placed completely inside the larger solenoid so that their long axes coincide. What is the mutual inductance of the two solenoids?

- A H
- B H
- C H
- D H
- E H

**Q8: **

A centrifuge with a radius of 20.0 cm is uniformly brought to rest from a rotation rate of rpm in a time of 30.0 s. A point is on the rim of the centrifuge and a line intersects both and the center of the centrifuge.

What is the magnitude of the total acceleration of the point at the instant ?

What is the magnitude of the angle between the direction of the total acceleration of the point and the line ?