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 straight wire 80 cm long lies at 30° to a uniform magnetic field of 0.5 T. The magnetic force on it is 1.2 N. Find the current I.

B = 0.5 TF = 1.2 NL = 80 cmθ = 30°

I = A

2.Easy

A flat circular coil of 25 turns and radius 5 cm carries a current of 2 A. Find the magnetic flux density B at its centre.

N = 25I = 2 AR = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

A proton moves on a circle in a uniform magnetic field of 0.25 T. Find the time T it takes for one revolution.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CB = 0.25 T

T = ns

4.Medium

A coil of 250 turns, area 150 cm² and resistance 4 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.2 T to 0.6 T in 50 ms. Find the average induced current I.

N = 250A = 150 cm²B: 0.2 T → 0.6 TΔt = 50 msR = 4 Ω

I = A

5.Hard

A short coil of 50 turns is wound tightly round the middle of a long solenoid of 1500 turns, length 25 cm and diameter 3 cm. The current in the solenoid changes at 20 A/s. Find the emf ε induced in the short coil.

N₁ = 1500N₂ = 50l = 25 cm⌀ = 3 cmdi/dt = 20 A/sμ₀ = 4π × 10⁻⁷ T·m/A

ε = mV

6.Hard

A coil of 100 turns, 12 cm × 10 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 39.99 V?

N = 100A = 12 cm × 10 cmB = 0.25 TE_rms = 39.99 V

n = rpm

Answer key

1. I = 6 A
2. B = 628.3 µT
3. T = 262.5 ns
4. I = 7.5 A
5. ε = 5.33 mV
6. n = 1800 rpm

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