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 4 A. At what distance r from the wire is the magnetic flux density 8 µT?

I = 4 AB = 8 µTμ₀ = 4π × 10⁻⁷ T·m/A

r = cm

2.Easy

A straight wire 100 cm long carries 20 A at an angle of 60° to a uniform magnetic field of 1.2 T. Find the magnitude of the force F on the wire.

B = 1.2 TI = 20 AL = 100 cmθ = 60°

F = N

3.Medium

An alpha particle moving at 6 × 10⁵ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 1.244 cm. Find the magnetic flux density B.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 6 × 10⁵ m/sr = 1.244 cm

B = T

4.Medium

A metal rod 20 cm long slides at 1 m/s along two rails in a uniform field of 0.25 T into the page. The rails are joined by a resistor of 0.5 Ω; the rod and rails have negligible resistance. Find the force F needed to keep the rod moving at constant speed (no friction).

B = 0.25 TL = 20 cmv = 1 m/sR = 0.5 Ω

F = mN

5.Hard

The current in a 500 mH inductor changes steadily from 1 A to 4 A in 10 ms. Find the magnitude of the self-induced emf ε.

L = 500 mH1 A → 4 AΔt = 10 ms

ε = V

6.Hard

A long air-core solenoid has 2000 turns, a length of 15 cm and a diameter of 2 cm. Find the energy W stored in its magnetic field when it carries 1 A.

N = 2000l = 15 cm⌀ = 2 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = mJ

Answer key

1. r = 10 cm
2. F = 20.78 N
3. B = 1 T
4. F = 5 mN
5. ε = 150 V
6. W = 5.264 mJ

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