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Worksheet: Mutual Inductance of Conducting Loops

Q1:

A coil of 40 turns is wrapped around a long solenoid of cross-sectional area 7 . 5 × 1 0 3 m2. The solenoid is 0.50 m long and has 500 turns.

What is the mutual inductance of this system?

  • A 3 . 2 × 1 0 4 H
  • B 2 . 6 × 1 0 4 H
  • C 4 . 5 × 1 0 4 H
  • D 3 . 8 × 1 0 4 H
  • E 4 . 7 × 1 0 4 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 3 . 8 × 1 0 4 H
  • B 4 . 5 × 1 0 4 H
  • C 4 . 2 × 1 0 4 H
  • D 3 . 3 × 1 0 4 H
  • E 5 . 0 × 1 0 4 H

Q2:

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

Q3:

An emf of 9 . 7 × 1 0 3 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 2 . 0 × 1 0 3 H
  • B 1 . 6 × 1 0 3 H
  • C 2 . 8 × 1 0 3 H
  • D 3 . 6 × 1 0 3 H
  • E 3 . 2 × 1 0 3 H

Q4:

When the current in one coil changes at a rate of 3.1 A/s, an emf of 9 . 7 × 1 0 3 V is induced in a second nearby coil. What is the mutual inductance of the two coils?

  • A 4 6 × 1 0 3 H
  • B 3 . 9 × 1 0 3 H
  • C 8 9 × 1 0 3 H
  • D 3 . 1 × 1 0 3 H
  • E 9 . 7 × 1 0 3 H

Q5:

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 3 6 × 1 0 6 H
  • B 9 . 6 × 1 0 6 H
  • C 9 8 × 1 0 6 H
  • D 2 . 5 × 1 0 6 H
  • E 3 . 1 × 1 0 6 H

Q6:

A solenoid of 𝑁 = 2 0 0 1 turns has length 𝑙 = 1 . 1 1 m and radius 𝑅 = 5 0 1 c m , and a second, smaller solenoid of 𝑁 = 1 0 0 2 turns has length 𝑙 = 0 . 9 0 2 m and radius 𝑅 = 2 5 2 c m . 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 4 . 3 × 1 0 3 H
  • B 3 . 1 × 1 0 3 H
  • C 6 . 6 × 1 0 3 H
  • D 5 . 5 × 1 0 3 H
  • E 4 . 8 × 1 0 3 H

Q7:

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 0 0 0 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 3 . 3 × 1 0 5 H
  • B 2 . 8 × 1 0 5 H
  • C 3 . 7 × 1 0 5 H
  • D 2 . 3 × 1 0 5 H
  • E 4 . 0 × 1 0 5 H

Q8:

A centrifuge with a radius of 20.0 cm is uniformly brought to rest from a rotation rate of 1 0 0 0 0 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 = 2 9 . 0 s ?

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