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 7.5×10 m2. The solenoid is 0.50 m long and has 500 turns.

What is the mutual inductance of this system?

  • A2.6×10 H
  • B3.2×10 H
  • C3.8×10 H
  • D4.7×10H
  • E4.5×10 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?

  • A3.8×10 H
  • B4.5×10 H
  • C4.2×10H
  • D3.3×10H
  • E5.0×10 H

Q2:

An emf of 9.7×10 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?

  • A1.6×10 H
  • B3.6×10 H
  • C2.8×10 H
  • D2.0×10 H
  • E3.2×10 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.

  • A2.8×10 H
  • B3.7×10 H
  • C3.3×10 H
  • D2.3×10 H
  • E4.0×10H

Q4:

When the current in one coil changes at a rate of 3.1 A/s, an emf of 9.7×10 V is induced in a second nearby coil. What is the mutual inductance of the two coils?

  • A3.1×10 H
  • B3.9×10 H
  • C9.7×10 H
  • D46×10 H
  • E89×10 H

Q5:

Two coils close to each other have a mutual inductance of 36 mH. If the current in one coil decays according to 𝐼=𝐼𝑒, where 𝐼=8.0A and 𝛼=7.0×10s, what is the emf induced in the second coil immediately after the current starts to decay at 𝑡=2.0×10s?

  • A1.7×10 V
  • B5.2×10 V
  • C8.7×10 V
  • D0.61×10 V
  • E12×10 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?

  • A36×10 H
  • B9.6×10 H
  • C2.5×10 H
  • D98×10 H
  • E3.1×10 H

Q7:

A solenoid of 𝑁=200 turns has length 𝑙=1.1m and radius 𝑅=50cm, and a second, smaller solenoid of 𝑁=100 turns has length 𝑙=0.90m and radius 𝑅=25cm. 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?

  • A5.5×10 H
  • B4.3×10 H
  • C6.6×10 H
  • D4.8×10 H
  • E3.1×10 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 𝑃 is on the rim of the centrifuge and a line 𝐿 intersects both 𝑃 and the center of the centrifuge.

What is the magnitude of the total acceleration of the point 𝑃 at the instant 𝑡=29.0s?

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

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