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

An alpha particle moves at 1 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.05 T. Find the magnitude of the magnetic force F on it.

|q| = 3.204 × 10⁻¹⁹ Cv = 1 × 10⁶ m/sB = 0.05 Tθ = 90°

F = fN

2.Easy

A straight wire 80 cm long carries 3 A at an angle of 45° to a uniform magnetic field of 0.4 T. Find the magnitude of the force F on the wire.

B = 0.4 TI = 3 AL = 80 cmθ = 45°

F = N

3.Medium

A metal rod 60 cm long slides at 8 m/s along two rails in a uniform field of 0.25 T into the page. Find the induced emf ε between its ends.

B = 0.25 TL = 60 cmv = 8 m/s

ε = V

4.Medium

An alpha particle moves at 5 × 10⁶ 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 = 5 × 10⁶ m/sB = 1 T

r = cm

5.Hard

A short coil of 200 turns is wound tightly round the middle of a long solenoid of 1500 turns, length 40 cm and diameter 4 cm. Find their mutual inductance M.

N₁ = 1500N₂ = 200l = 40 cm⌀ = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A

M = mH

6.Hard

A coil of 150 turns, 15 cm × 20 cm, rotates at 1200 rpm in a uniform field of 0.25 T about an axis perpendicular to the field. Find the peak emf E₀.

N = 150A = 15 cm × 20 cmB = 0.25 Tn = 1200 rpm

E₀ = V

Answer key

1. F = 16.02 fN
2. F = 0.6788 N
3. ε = 1.2 V
4. r = 10.37 cm
5. M = 1.184 mH
6. E₀ = 141.4 V

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