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 = 12.57 mTI = 1 AL = 12 cmN = ?

A solenoid 12 cm long carries 1 A. How many turns N must it have for a flux density of 12.57 mT inside?

I = 1 AL = 12 cmB = 12.57 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
2.Easy
B = ?I = 4 AL = 12 cmN = 600

A solenoid 12 cm long has 600 turns and carries 4 A. Find the magnetic flux density B inside it, far from the ends.

N = 600L = 12 cmI = 4 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
3.Medium
nBA = 100 cm², N = 500B: 0 → 0.2 T

A coil of 500 turns has an area of 100 cm². A uniform field perpendicular to the coil rises steadily from 0 T to 0.2 T in 250 ms. Find the average induced emf ε.

N = 500A = 100 cm²B: 0 T → 0.2 TΔt = 250 ms
ε = V
4.Medium
nBA = 25 cm², N = 25B = 0.5 T

A coil of 25 turns has an area of 25 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.5 T, which is perpendicular to its plane, in 40 ms. Find the average induced emf ε.

N = 25A = 25 cm²B = 0.5 TΔt = 40 ms
ε = V
5.Hard
Bn = 300 rpm5 cm × 10 cmN = 50B = 0.3 T

A coil of 50 turns, 5 cm × 10 cm, rotates at 300 rpm in a uniform field of 0.3 T about an axis perpendicular to the field. Find the rms value Erms of the emf.

N = 50A = 5 cm × 10 cmB = 0.3 Tn = 300 rpm
Erms = V
6.Hard
Bn = 300 rpm20 cm × 5 cmN = 100B = 0.25 T

A coil of 100 turns, 20 cm × 5 cm, rotates at 300 rpm in a uniform field of 0.25 T about an axis perpendicular to the field. Find the rms value Erms of the emf.

N = 100A = 20 cm × 5 cmB = 0.25 Tn = 300 rpm
Erms = V

Answer key

  1. 1. N = 1200
  2. 2. B = 25.13 mT
  3. 3. ε = 4 V
  4. 4. ε = 1.563 V
  5. 5. Erms = 1.666 V
  6. 6. Erms = 5.554 V

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