Worksheet: Self-Inductance of an Inductor

In this worksheet, we will practice calculating a conducting loop's self-inductance from the change rates of emf induced in it and the magnetic field produced by the loop.

Q1:

A coil with a self-inductance of 3.0 H carries a current that decreases at a uniform rate d/d𝐼𝑡=0.050 A/s. What is the emf induced in the coil?

Q2:

What is the self-inductance per meter of a coaxial cable whose inner radius is 0.500 mm and whose outer radius is 4.00 mm?

  • A 3 . 9 3 × 0 H/m
  • B 3 . 2 9 × 1 0 H/m
  • C 4 . 1 6 × 1 0 H/m
  • D 2 . 9 8 × 1 0 H/m
  • E 3 . 6 0 × 1 0 H/m

Q3:

An emf of 0.40 V is induced across a coil by changing the current through it. The current changes uniformly from 0.10 A to 0.60 A in 0.30 s. What is the self-inductance of the coil?

Q4:

A 25.0-H inductor has 100 A of current turned off in 1.00 ms. What voltage is induced to oppose this?

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

Q5:

What is the rate at which the current though a 0.30-H coil is changing if an emf of 0.12 V is induced across the coil?

Q6:

The current 𝐼(𝑡) through a 7.0 mH inductor varies with time, as shown in the figure. The resistance of the inductor is 4.0 Ω.

Calculate the voltage across the inductor from 𝑡=0.0 to 𝑡=3.0ms.

Calculate the voltage across the inductor from 𝑡=3.0ms to 𝑡=6.0ms.

Calculate the voltage across the inductor from 𝑡=6.0ms to 𝑡=12.0ms.

Q7:

Two long, parallel wires of length 1.5 cm carry equal currents in opposite directions. The radius of each wire is 30 cm, and the distance between the centers of the wires is 90 cm. Find the self-inductance of the wires.

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