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 10 A. Find the magnetic flux density B at point P, 1 cm from the wire.

I = 10 Ar = 1 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A single circular loop of wire with radius 8 cm carries a current of 0.5 A. Find the magnetic flux density B at its centre.

N = 1I = 0.5 AR = 8 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

A coil of 20 turns, area 50 cm² and resistance 2 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.55 T in 200 ms. Find the average induced current I.

N = 20A = 50 cm²B: 0.05 T → 0.55 TΔt = 200 msR = 2 Ω

I = mA

4.Medium

An alpha particle moves at 2 × 10⁵ m/s perpendicular to a uniform magnetic field of 1 T. Find the radius r of its circular path.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 2 × 10⁵ m/sB = 1 T

r = cm

5.Hard

A coil of 250 turns, 10 cm × 15 cm, rotates in a uniform field of 0.1 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 49.98 V?

N = 250A = 10 cm × 15 cmB = 0.1 TE_rms = 49.98 V

n = rpm

6.Hard

The current in a 10 mH inductor changes steadily from 2.5 A to 2 A in 2 ms. Find the magnitude of the self-induced emf ε.

L = 10 mH2.5 A → 2 AΔt = 2 ms

ε = V

Answer key

1. B = 200 µT
2. B = 3.927 µT
3. I = 125 mA
4. r = 0.4148 cm
5. n = 1800 rpm
6. ε = 2.5 V

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