Magnetic fields & induction worksheet with answers

Free printable Magnetic fields & induction worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A long straight wire carries a current of 2 A. Find the magnetic flux density B at point P, 2.5 cm from the wire.

I = 2 Ar = 2.5 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A flat circular coil of 20 turns and radius 15 cm carries a current of 4 A. Find the magnetic flux density B at its centre.

N = 20I = 4 AR = 15 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

An alpha particle moving at 1 × 10⁶ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 8.296 cm. Find the magnetic flux density B.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 1 × 10⁶ m/sr = 8.296 cm

B = T

4.Medium

A coil of 500 turns has an area of 80 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.2 T, which is perpendicular to its plane, in 40 ms. Find the average induced emf ε.

N = 500A = 80 cm²B = 0.2 TΔt = 40 ms

ε = V

5.Hard

A short coil of 50 turns is wound tightly round the middle of a long solenoid of 2000 turns, length 30 cm and diameter 2 cm. Find their mutual inductance M.

N₁ = 2000N₂ = 50l = 30 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A

M = µH

6.Hard

A coil of 150 turns, 10 cm × 25 cm, rotates in a uniform field of 0.25 T about an axis perpendicular to the field. At what speed n (in revolutions per minute) must it turn to give an rms emf of 208.3 V?

N = 150A = 10 cm × 25 cmB = 0.25 TE_rms = 208.3 V

n = rpm

Answer key

1. B = 16 µT
2. B = 335.1 µT
3. B = 0.25 T
4. ε = 40 V
5. M = 131.6 µH
6. n = 3001 rpm

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