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 = 2.5 AR = 6 cmB = ?N = 50

A flat circular coil of 50 turns and radius 6 cm carries a current of 2.5 A. Find the magnetic flux density B at its centre.

N = 50I = 2.5 AR = 6 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
2.Easy
I = 1.5 AR = 10 cmB = ?N = 25

A flat circular coil of 25 turns and radius 10 cm carries a current of 1.5 A. Find the magnetic flux density B at its centre.

N = 25I = 1.5 AR = 10 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
R = 0.5 Ωv = 10 m/sL = 25 cmB = 0.6 T

A metal rod 25 cm long slides at 10 m/s along two rails in a uniform field of 0.6 T into the page. The rails are joined by a resistor of 0.5 Ω; the rod and rails have negligible resistance. Find the force F needed to keep the rod moving at constant speed (no friction).

B = 0.6 TL = 25 cmv = 10 m/sR = 0.5 Ω
F = mN
4.Medium
10 A20 Ad = 3 cm

Two long parallel wires 3 cm apart carry currents of 10 A and 20 A in the same direction. Find the force per metre of length F/L between them.

I1 = 10 AI2 = 20 Ad = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A
F/L = µN/m
5.Hard
Bn = ?8 cm × 5 cmN = 20B = 0.5 T

A coil of 20 turns, 8 cm × 5 cm, rotates in a uniform field of 0.5 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 5.331 V?

N = 20A = 8 cm × 5 cmB = 0.5 TErms = 5.331 V
n = rpm
6.Hard
L1​ = 80 mH1000 A/sL2​ = 10 mHk = 0.75ε = ?

Two coils with self-inductances of 80 mH and 10 mH have a coupling coefficient of 0.75. The current in the first coil changes at 1000 A/s. Find the emf ε induced in the second coil.

L1 = 80 mHL2 = 10 mHk = 0.75di/dt = 1000 A/s
ε = V

Answer key

  1. 1. B = 1.309 mT
  2. 2. B = 235.6 µT
  3. 3. F = 450 mN
  4. 4. F/L = 1333 µN/m
  5. 5. n = 1800 rpm
  6. 6. ε = 21.21 V

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