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 proton moves at 2.5 × 10⁶ m/s at an angle of 45° 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 = 2.5 × 10⁶ m/sB = 0.8 Tθ = 45°

F = fN

2.Easy

A solenoid 30 cm long has 1200 turns and carries 2 A. Find the magnetic flux density B inside it, far from the ends.

N = 1200L = 30 cmI = 2 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

3.Medium

A proton moves on a circle in a uniform magnetic field of 0.2 T. Find the time T it takes for one revolution.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CB = 0.2 T

T = ns

4.Medium

A proton moves at 8 × 10⁶ m/s perpendicular to a uniform magnetic field of 1 T. Find the radius r of its circular path.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 8 × 10⁶ m/sB = 1 T

r = cm

5.Hard

In a velocity selector, crossed fields E = 2 × 10⁵ V/m and B = 0.5 T let only ions of one speed pass straight through. Find that speed v.

E = 2 × 10⁵ V/mB₁ = 0.5 T

v = m/s

6.Hard

A coil of 100 turns, 5 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 6.942 V?

N = 100A = 5 cm × 25 cmB = 0.25 TE_rms = 6.942 V

n = rpm

Answer key

1. F = 226.6 fN
2. B = 10.05 mT
3. T = 328.1 ns
4. r = 8.355 cm
5. v = 400000 m/s
6. n = 300 rpm

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