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 = 1.5 AR = 12 cmB = ?N = 10

A flat circular coil of 10 turns and radius 12 cm carries a current of 1.5 A. Find the magnetic flux density B at its centre.

N = 10I = 1.5 AR = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
2.Easy
−v = 2.5 × 10⁶ m/sB = 0.2 T

An electron moves at 2.5 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.2 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 2.5 × 10⁶ m/sB = 0.2 Tθ = 90°
F = fN
3.Medium
+v = 3 × 10⁵ m/sB = 0.25 T

An alpha particle moves on a circle in a uniform magnetic field of 0.25 T. Find the time T it takes for one revolution.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CB = 0.25 T
T = ns
4.Medium
R = 5 Ωv = 8 m/sL = 80 cmB = 1 T

A metal rod 80 cm long slides at 8 m/s along two rails in a uniform field of 1 T into the page. The rails are joined by a resistor of 5 Ω; the rod and rails have negligible resistance. Find the current I.

B = 1 TL = 80 cmv = 8 m/sR = 5 Ω
I = A
5.Hard
L1​ = 50 mH20 A/sL2​ = 10 mHk = 0.9ε = ?

Two coils with self-inductances of 50 mH and 10 mH have a coupling coefficient of 0.9. The current in the first coil changes at 20 A/s. Find the emf ε induced in the second coil.

L1 = 50 mHL2 = 10 mHk = 0.9di/dt = 20 A/s
ε = V
6.Hard
I = 1 Al = 10 cmN = 200, ⌀ 3 cm

A long air-core solenoid has 200 turns, a length of 10 cm and a diameter of 3 cm. Find the energy W stored in its magnetic field when it carries 1 A.

N = 200l = 10 cm⌀ = 3 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A
W = µJ

Answer key

  1. 1. B = 78.54 µT
  2. 2. F = 80.1 fN
  3. 3. T = 521.2 ns
  4. 4. I = 1.28 A
  5. 5. ε = 0.4025 V
  6. 6. W = 177.7 µJ

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