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 solenoid 50 cm long has 1000 turns and carries 3 A. Find the magnetic flux density B inside it, far from the ends.

N = 1000L = 50 cmI = 3 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

2.Easy

A flat circular coil of 5 turns and radius 10 cm carries a current of 1 A. Find the magnetic flux density B at its centre.

N = 5I = 1 AR = 10 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

Two long parallel wires 12 cm apart carry currents of 12 A and 20 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 12 AI₂ = 20 Ad = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

A coil of 10 turns, area 80 cm² and resistance 10 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0 T to 0.5 T in 10 ms. Find the average induced current I.

N = 10A = 80 cm²B: 0 T → 0.5 TΔt = 10 msR = 10 Ω

I = mA

5.Hard

A coil of 200 turns, 20 cm × 10 cm, rotates in a uniform field of 0.3 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 26.66 V?

N = 200A = 20 cm × 10 cmB = 0.3 TE_rms = 26.66 V

n = rpm

6.Hard

A coil of 20 turns, 8 cm × 10 cm, rotates at 3600 rpm in a uniform field of 0.25 T about an axis perpendicular to the field. Find the rms value E_rms of the emf.

N = 20A = 8 cm × 10 cmB = 0.25 Tn = 3600 rpm

E_rms = V

Answer key

1. B = 7.54 mT
2. B = 31.42 µT
3. F/L = 400 µN/m
4. I = 400 mA
5. n = 300 rpm
6. E_rms = 10.66 V

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