Worksheet: Magnetic Field of a Toroid

In this worksheet, we will practice using the Biot–Savart law and Ampere's law to calculate the magnetic field produced by a toroid.

Q1:

A toroid with a square cross section 3 . 0 × 3 . 0 c m c m has an inner radius of 25.0 cm. It is wound with 500 turns of wire, and it carries a current of 2.0 A. What is the strength of the magnetic field at the centre of the square cross section?

  • A 0.67 mT
  • B 0.90 mT
  • C 0.50 mT
  • D 0.80 mT
  • E 0.33 mT

Q2:

A toroid has an inner radius of 20.0 cm and an outer radius of 22.0 cm. The toroid is tightly wound with one layer of 0.250-mm-diameter wire.

How many turns are there on the toroid?

  • A 5 1 9 8 6
  • B 5 1 5 6 8
  • C 5 2 0 7 8
  • D 5 2 7 7 8
  • E 5 2 4 6 4

If the current through the toroid windings is 2.0 A, what is the strength of the magnetic field at the centre of the toroid?

  • A 0.10 T
  • B 0.25 T
  • C 0.20 T
  • D 0.16 T
  • E 0.32 T

Q3:

There is a current of 1.5 A through the windings of a large, thin toroid with 200 turns per meter. If the toroid is filled with iron for which the magnetic susceptibility is , what is the magnetic field within it?

  • A T
  • B T
  • C
  • D T
  • E T

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