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 = ?I = 1 AL = 30 cmN = 400

A solenoid 30 cm long has 400 turns and carries 1 A. Find the magnetic flux density B inside it, far from the ends.

N = 400L = 30 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
2.Easy
B0.25 T12 A30°L = 50 cm

A straight wire 50 cm long carries 12 A at an angle of 30° to a uniform magnetic field of 0.25 T. Find the magnitude of the force F on the wire.

B = 0.25 TI = 12 AL = 50 cmθ = 30°
F = N
3.Medium
+v = 8 × 10⁶ m/sB = 0.4 T

A proton moves on a circle in a uniform magnetic field of 0.4 T. Find the time T it takes for one revolution.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CB = 0.4 T
T = ns
4.Medium
nBA = 100 cm², N = 20B: 0.05 → 0.65 T

A coil of 20 turns has an area of 100 cm². A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.65 T in 500 ms. Find the average induced emf ε.

N = 20A = 100 cm²B: 0.05 T → 0.65 TΔt = 500 ms
ε = mV
5.Hard
L = 500 mH2 → 0.5 A

The current in a 500 mH inductor changes steadily from 2 A to 0.5 A in 10 ms. Find the magnitude of the self-induced emf ε.

L = 500 mH2 A → 0.5 AΔt = 10 ms
ε = V
6.Hard
I = 4 Al = 10 cmN = 1500, ⌀ 2 cm

A long air-core solenoid has 1500 turns, a length of 10 cm and a diameter of 2 cm. Find the energy W stored in its magnetic field when it carries 4 A.

N = 1500l = 10 cm⌀ = 2 cmI = 4 Aμ₀ = 4π × 10⁻⁷ T·m/A
W = mJ

Answer key

  1. 1. B = 1.676 mT
  2. 2. F = 0.75 N
  3. 3. T = 164 ns
  4. 4. ε = 240 mV
  5. 5. ε = 75 V
  6. 6. W = 71.06 mJ

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