# 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 m2. 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
• E H

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 cm2; it is wound uniformly with 1,000 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 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 10,000 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 ?