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

The magnetic flux density 6 cm from a long straight wire is 16.67 µT. Find the current I in the wire.

B = 16.67 µTr = 6 cmμ₀ = 4π × 10⁻⁷ T·m/A

I = A

2.Easy

A solenoid 40 cm long has 1000 turns and carries 2 A. Find the magnetic flux density B inside it, far from the ends.

N = 1000L = 40 cmI = 2 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

3.Medium

A metal rod 30 cm long slides at 3 m/s along two rails in a uniform field of 1 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 = 1 TL = 30 cmv = 3 m/sR = 0.5 Ω

F = mN

4.Medium

A proton moves at 1 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.4 T. Find the radius r of its circular path.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 1 × 10⁵ m/sB = 0.4 T

r = cm

5.Hard

A long air-core solenoid has 200 turns, a length of 50 cm and a diameter of 2.5 cm. Find the energy W stored in its magnetic field when it carries 1.5 A.

N = 200l = 50 cm⌀ = 2.5 cmI = 1.5 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

6.Hard

A coil of 250 turns, 8 cm × 25 cm, rotates at 1800 rpm in a uniform field of 0.1 T about an axis perpendicular to the field. Find the rms value E_rms of the emf.

N = 250A = 8 cm × 25 cmB = 0.1 Tn = 1800 rpm

E_rms = V

Answer key

1. I = 5.001 A
2. B = 6.283 mT
3. F = 540 mN
4. r = 0.2611 cm
5. W = 55.52 µJ
6. E_rms = 66.64 V

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