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
+v = 4 × 10⁶ m/sB = 0.05 T

A proton moves at 4 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.05 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 4 × 10⁶ m/sB = 0.05 Tθ = 90°
F = fN
2.Easy
B = ?I = 0.5 AL = 20 cmN = 1200

A solenoid 20 cm long has 1200 turns and carries 0.5 A. Find the magnetic flux density B inside it, far from the ends.

N = 1200L = 20 cmI = 0.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
3.Medium
R = 0.5 Ωv = 3 m/sL = 40 cmB = 0.4 T

A metal rod 40 cm long slides at 3 m/s along two rails in a uniform field of 0.4 T into the page. The rails are joined by a resistor of 0.5 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.4 TL = 40 cmv = 3 m/sR = 0.5 Ω
P = mW
4.Medium
+v = 3 × 10⁵ m/sB = 0.5 T

An alpha particle moves on a circle in a uniform magnetic field of 0.5 T. Find the time T it takes for one revolution.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CB = 0.5 T
T = ns
5.Hard
Bn = ?12 cm × 25 cmN = 100B = 0.2 T

A coil of 100 turns, 12 cm × 25 cm, rotates in a uniform field of 0.2 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 133.3 V?

N = 100A = 12 cm × 25 cmB = 0.2 TErms = 133.3 V
n = rpm
6.Hard
L = 25 mH0 → 1 A

The current in a 25 mH inductor changes steadily from 0 A to 1 A in 10 ms. Find the magnitude of the self-induced emf ε.

L = 25 mH0 A → 1 AΔt = 10 ms
ε = V

Answer key

  1. 1. F = 32.04 fN
  2. 2. B = 3.77 mT
  3. 3. P = 460.8 mW
  4. 4. T = 260.6 ns
  5. 5. n = 3000 rpm
  6. 6. ε = 2.5 V

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