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 long straight wire carries a current of 25 A. Find the magnetic flux density B at point P, 2.5 cm from the wire.

I = 25 Ar = 2.5 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A flat circular coil of 10 turns and radius 6 cm carries a current of 2 A. Find the magnetic flux density B at its centre.

N = 10I = 2 AR = 6 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

A coil of 50 turns has an area of 50 cm². A uniform field perpendicular to the coil rises steadily from 0 T to 0.1 T in 40 ms. Find the average induced emf ε.

N = 50A = 50 cm²B: 0 T → 0.1 TΔt = 40 ms

ε = mV

4.Medium

An alpha particle moving at 3 × 10⁵ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 3.111 cm. Find the magnetic flux density B.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 3 × 10⁵ m/sr = 3.111 cm

B = T

5.Hard

A short coil of 100 turns is wound tightly round the middle of a long solenoid of 2000 turns, length 40 cm and diameter 4 cm. The current in the solenoid changes at 100 A/s. Find the emf ε induced in the short coil.

N₁ = 2000N₂ = 100l = 40 cm⌀ = 4 cmdi/dt = 100 A/sμ₀ = 4π × 10⁻⁷ T·m/A

ε = mV

6.Hard

A coil of 50 turns, 12 cm × 20 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 13.33 V?

N = 50A = 12 cm × 20 cmB = 0.5 TE_rms = 13.33 V

n = rpm

Answer key

1. B = 200 µT
2. B = 209.4 µT
3. ε = 625 mV
4. B = 0.2 T
5. ε = 78.96 mV
6. n = 300 rpm

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