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 rectangular loop of 20 cm by 25 cm lies in a uniform magnetic field of 0.4 T. The field makes an angle of 60° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.4 TA = 20 cm × 25 cm60° to the normal

Φ = mWb

2.Easy

An electron moves at 1.5 × 10⁶ m/s at an angle of 30° to a uniform magnetic field of 0.8 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 1.5 × 10⁶ m/sB = 0.8 Tθ = 30°

F = fN

3.Medium

Two long parallel wires 8 cm apart carry currents of 8 A and 20 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 8 AI₂ = 20 Ad = 8 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

An alpha particle moves at 4 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.8 T. Find the radius r of its circular path.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 4 × 10⁶ m/sB = 0.8 T

r = cm

5.Hard

A long air-core solenoid has 500 turns, a length of 40 cm and a diameter of 1 cm. Find the energy W stored in its magnetic field when it carries 2 A.

N = 500l = 40 cm⌀ = 1 cmI = 2 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

6.Hard

A coil of 200 turns, 15 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 249.9 V?

N = 200A = 15 cm × 25 cmB = 0.25 TE_rms = 249.9 V

n = rpm

Answer key

1. Φ = 10 mWb
2. F = 96.12 fN
3. F/L = 400 µN/m
4. r = 10.37 cm
5. W = 123.4 µJ
6. n = 1800 rpm

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