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 solenoid 40 cm long has 800 turns and carries 1 A. Find the magnetic flux density B inside it, far from the ends.

N = 800L = 40 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

2.Easy

A single circular loop of wire with radius 5 cm carries a current of 4 A. Find the magnetic flux density B at its centre.

N = 1I = 4 AR = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

A metal rod 40 cm long slides at 1 m/s along two rails in a uniform field of 0.1 T into the page. Find the induced emf ε between its ends.

B = 0.1 TL = 40 cmv = 1 m/s

ε = mV

4.Medium

Two long parallel wires 10 cm apart carry currents of 5 A and 15 A in opposite directions. Find the magnitude of the magnetic flux density B at point P, halfway between them.

I₁ = 5 AI₂ = 15 Ad = 10 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

5.Hard

A coil of 250 turns, 20 cm × 20 cm, rotates in a uniform field of 0.2 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 266.6 V?

N = 250A = 20 cm × 20 cmB = 0.2 TE_rms = 266.6 V

n = rpm

6.Hard

A short coil of 200 turns is wound tightly round the middle of a long solenoid of 2000 turns, length 20 cm and diameter 4 cm. The current in the solenoid changes at 20 A/s. Find the emf ε induced in the short coil.

N₁ = 2000N₂ = 200l = 20 cm⌀ = 4 cmdi/dt = 20 A/sμ₀ = 4π × 10⁻⁷ T·m/A

ε = mV

Answer key

1. B = 2.513 mT
2. B = 50.27 µT
3. ε = 40 mV
4. B = 80 µT
5. n = 1800 rpm
6. ε = 63.17 mV

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