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
I = 3 AR = 5 cmB = ?N = 10

A flat circular coil of 10 turns and radius 5 cm carries a current of 3 A. Find the magnetic flux density B at its centre.

N = 10I = 3 AR = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
2.Easy
−v = 4 × 10⁶ m/sB = 0.02 T

An electron moves at 4 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.02 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 4 × 10⁶ m/sB = 0.02 Tθ = 90°
F = fN
3.Medium
nBA = 50 cm², N = 250B: 0 → 0.4 T

A coil of 250 turns has an area of 50 cm². A uniform field perpendicular to the coil rises steadily from 0 T to 0.4 T in 10 ms. Find the average induced emf ε.

N = 250A = 50 cm²B: 0 T → 0.4 TΔt = 10 ms
ε = V
4.Medium
+v = 6 × 10⁵ m/sr = ?B = 1.5 T

An alpha particle moves at 6 × 10⁵ m/s perpendicular to a uniform magnetic field of 1.5 T. Find the radius r of its circular path.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 6 × 10⁵ m/sB = 1.5 T
r = cm
5.Hard
l = 50 cmN = 400, ⌀ 2 cm

A long air-core solenoid has 400 turns, a length of 50 cm and a diameter of 2 cm. Find its self-inductance L.

N = 400l = 50 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = µH
6.Hard
Bn = ?15 cm × 25 cmN = 150B = 0.4 T

A coil of 150 turns, 15 cm × 25 cm, rotates in a uniform field of 0.4 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 199.9 V?

N = 150A = 15 cm × 25 cmB = 0.4 TErms = 199.9 V
n = rpm

Answer key

  1. 1. B = 377 µT
  2. 2. F = 12.82 fN
  3. 3. ε = 50 V
  4. 4. r = 0.8296 cm
  5. 5. L = 126.3 µH
  6. 6. n = 1200 rpm

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