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
B = 41.89 mTI = 4 AL = 12 cmN = ?

A solenoid 12 cm long carries 4 A. How many turns N must it have for a flux density of 41.89 mT inside?

I = 4 AL = 12 cmB = 41.89 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
2.Easy
B0.8 T20 A90°L = 100 cm

A straight wire 100 cm long carries 20 A at an angle of 90° to a uniform magnetic field of 0.8 T. Find the magnitude of the force F on the wire.

B = 0.8 TI = 20 AL = 100 cmθ = 90°
F = N
3.Medium
nBA = 150 cm², N = 50B: 0 → 0.5 T

A coil of 50 turns, area 150 cm² and resistance 20 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0 T to 0.5 T in 20 ms. Find the average induced current I.

N = 50A = 150 cm²B: 0 T → 0.5 TΔt = 20 msR = 20 Ω
I = mA
4.Medium
nBA = 40 cm², N = 25B = 0.5 T

A coil of 25 turns has an area of 40 cm². The coil sits in a uniform field of 0.5 T perpendicular to its plane, and the field is switched off in 100 ms. Find the average induced emf ε.

N = 25A = 40 cm²B = 0.5 TΔt = 100 ms
ε = mV
5.Hard
L1​ = 50 mH100 A/sL2​ = 20 mHk = 0.8ε = ?

Two coils with self-inductances of 50 mH and 20 mH have a coupling coefficient of 0.8. The current in the first coil changes at 100 A/s. Find the emf ε induced in the second coil.

L1 = 50 mHL2 = 20 mHk = 0.8di/dt = 100 A/s
ε = V
6.Hard
l = 15 cmN = 500, ⌀ 3 cm

A long air-core solenoid has 500 turns, a length of 15 cm and a diameter of 3 cm. Find its self-inductance L.

N = 500l = 15 cm⌀ = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = mH

Answer key

  1. 1. N = 1000
  2. 2. F = 16 N
  3. 3. I = 937.5 mA
  4. 4. ε = 500 mV
  5. 5. ε = 2.53 V
  6. 6. L = 1.48 mH

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