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

A single circular loop of wire with radius 8 cm carries a current of 1 A. Find the magnetic flux density B at its centre.

N = 1I = 1 AR = 8 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A straight wire 50 cm long lies at 30° to a uniform magnetic field of 1.2 T. The magnetic force on it is 0.6 N. Find the current I.

B = 1.2 TF = 0.6 NL = 50 cmθ = 30°

I = A

3.Medium

A coil of 200 turns has an area of 200 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.1 T, which is perpendicular to its plane, in 20 ms. Find the average induced emf ε.

N = 200A = 200 cm²B = 0.1 TΔt = 20 ms

ε = V

4.Medium

A coil of 500 turns has an area of 200 cm². A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.25 T in 40 ms. Find the average induced emf ε.

N = 500A = 200 cm²B: 0.05 T → 0.25 TΔt = 40 ms

ε = V

5.Hard

A long air-core solenoid has 200 turns, a length of 40 cm and a diameter of 2.5 cm. Find the energy W stored in its magnetic field when it carries 5 A.

N = 200l = 40 cm⌀ = 2.5 cmI = 5 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

6.Hard

A short coil of 100 turns is wound tightly round the middle of a long solenoid of 1500 turns, length 30 cm and diameter 5 cm. The current in the solenoid changes at 20 A/s. Find the emf ε induced in the short coil.

N₁ = 1500N₂ = 100l = 30 cm⌀ = 5 cmdi/dt = 20 A/sμ₀ = 4π × 10⁻⁷ T·m/A

ε = mV

Answer key

1. B = 7.854 µT
2. I = 2 A
3. ε = 40 V
4. ε = 50 V
5. W = 771.1 µJ
6. ε = 24.67 mV

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