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 straight wire 20 cm long carries 2 A at an angle of 45° to a uniform magnetic field of 0.4 T. Find the magnitude of the force F on the wire.

B = 0.4 TI = 2 AL = 20 cmθ = 45°

F = N

2.Easy

A flat circular coil of 50 turns and radius 15 cm carries a current of 2.5 A. Find the magnetic flux density B at its centre.

N = 50I = 2.5 AR = 15 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

Two long parallel wires 3 cm apart carry currents of 5 A and 2 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 5 AI₂ = 2 Ad = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

A proton moves on a circle in a uniform magnetic field of 0.1 T. Find the time T it takes for one revolution.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CB = 0.1 T

T = ns

5.Hard

A long air-core solenoid has 1000 turns, a length of 40 cm and a diameter of 5 cm. Find the energy W stored in its magnetic field when it carries 5 A.

N = 1000l = 40 cm⌀ = 5 cmI = 5 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = mJ

6.Hard

Two coils with self-inductances of 40 mH and 100 mH have a coupling coefficient of 0.3. The current in the first coil changes at 50 A/s. Find the emf ε induced in the second coil.

L₁ = 40 mHL₂ = 100 mHk = 0.3di/dt = 50 A/s

ε = V

Answer key

1. F = 0.1131 N
2. B = 523.6 µT
3. F/L = 66.67 µN/m
4. T = 656.2 ns
5. W = 77.11 mJ
6. ε = 0.9487 V

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