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 = 5 × 10⁵ m/sB = 0.02 T

An alpha particle moves at 5 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.02 T. Find the magnitude of the magnetic force F on it.

|q| = 3.204 × 10⁻¹⁹ Cv = 5 × 10⁵ m/sB = 0.02 Tθ = 90°
F = fN
2.Easy
B = ?I = 2.5 AL = 12 cmN = 1200

A solenoid 12 cm long has 1200 turns and carries 2.5 A. Find the magnetic flux density B inside it, far from the ends.

N = 1200L = 12 cmI = 2.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
3.Medium
R = 1 Ωv = 6 m/sL = 30 cmB = 0.5 T

A metal rod 30 cm long slides at 6 m/s along two rails in a uniform field of 0.5 T into the page. The rails are joined by a resistor of 1 Ω; the rod and rails have negligible resistance. Find the force F needed to keep the rod moving at constant speed (no friction).

B = 0.5 TL = 30 cmv = 6 m/sR = 1 Ω
F = mN
4.Medium
nBA = 100 cm², N = 50B: 0 → 0.8 T

A coil of 50 turns, area 100 cm² and resistance 4 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0 T to 0.8 T in 100 ms. Find the average induced current I.

N = 50A = 100 cm²B: 0 T → 0.8 TΔt = 100 msR = 4 Ω
I = A
5.Hard
l = 30 cmN = 1000, ⌀ 2.5 cm

A long air-core solenoid has 1000 turns, a length of 30 cm and a diameter of 2.5 cm. Find its self-inductance L.

N = 1000l = 30 cm⌀ = 2.5 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = mH
6.Hard
L = 500 mH0.5 → 5.5 A

The current in a 500 mH inductor changes steadily from 0.5 A to 5.5 A in 50 ms. Find the magnitude of the self-induced emf ε.

L = 500 mH0.5 A → 5.5 AΔt = 50 ms
ε = V

Answer key

  1. 1. F = 3.204 fN
  2. 2. B = 31.42 mT
  3. 3. F = 135 mN
  4. 4. I = 1 A
  5. 5. L = 2.056 mH
  6. 6. ε = 50 V

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