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 flat circular coil of 20 turns and radius 10 cm carries a current of 5 A. Find the magnetic flux density B at its centre.

N = 20I = 5 AR = 10 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

An electron moves at 4 × 10⁶ m/s perpendicular to a uniform magnetic field of 1.5 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 4 × 10⁶ m/sB = 1.5 Tθ = 90°

F = fN

3.Medium

Two long parallel wires 4 cm apart carry currents of 12 A and 12 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 12 AI₂ = 12 Ad = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

A metal rod 40 cm long slides at 1 m/s along two rails in a uniform field of 0.5 T into the page. The rails are joined by a resistor of 2.5 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.5 TL = 40 cmv = 1 m/sR = 2.5 Ω

I = mA

5.Hard

A long air-core solenoid has 100 turns, a length of 10 cm and a diameter of 2.5 cm. Find the energy W stored in its magnetic field when it carries 3 A.

N = 100l = 10 cm⌀ = 2.5 cmI = 3 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

6.Hard

The current in a 500 mH inductor changes steadily from 2 A to 4 A in 1 ms. Find the magnitude of the self-induced emf ε.

L = 500 mH2 A → 4 AΔt = 1 ms

ε = V

Answer key

1. B = 628.3 µT
2. F = 961.2 fN
3. F/L = 720 µN/m
4. I = 80 mA
5. W = 277.6 µJ
6. ε = 1000 V

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