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 30 cm long lies at 90° to a uniform magnetic field of 0.25 T. The magnetic force on it is 0.9 N. Find the current I.

B = 0.25 TF = 0.9 NL = 30 cmθ = 90°

I = A

2.Easy

A proton moves at 6 × 10⁶ m/s at an angle of 60° to a uniform magnetic field of 0.1 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 6 × 10⁶ m/sB = 0.1 Tθ = 60°

F = fN

3.Medium

A metal rod 20 cm long slides at 8 m/s along two rails in a uniform field of 0.8 T into the page. The rails are joined by a resistor of 5 Ω; the rod and rails have negligible resistance. Find the force F needed to keep the rod moving at constant speed (no friction).

B = 0.8 TL = 20 cmv = 8 m/sR = 5 Ω

F = mN

4.Medium

Two long parallel wires 8 cm apart carry currents of 8 A and 25 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 8 AI₂ = 25 Ad = 8 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

5.Hard

The current in an 80 mH inductor changes steadily from 5.5 A to 0.5 A in 50 ms. Find the magnitude of the self-induced emf ε.

L = 80 mH5.5 A → 0.5 AΔt = 50 ms

ε = V

6.Hard

A long air-core solenoid has 1000 turns, a length of 50 cm and a diameter of 5 cm. Find the energy W stored in its magnetic field when it carries 3 A.

N = 1000l = 50 cm⌀ = 5 cmI = 3 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = mJ

Answer key

1. I = 12 A
2. F = 83.24 fN
3. F = 40.96 mN
4. F/L = 500 µN/m
5. ε = 8 V
6. W = 22.21 mJ

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