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 single circular loop of wire with radius 8 cm carries a current of 4 A. Find the magnetic flux density B at its centre.

N = 1I = 4 AR = 8 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A solenoid 15 cm long has 600 turns. Which current I gives a magnetic flux density of 20.11 mT inside it?

N = 600L = 15 cmB = 20.11 mTμ₀ = 4π × 10⁻⁷ T·m/A

I = A

3.Medium

A proton moving at 2 × 10⁵ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 0.8355 cm. Find the magnetic flux density B.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 2 × 10⁵ m/sr = 0.8355 cm

B = T

4.Medium

A metal rod 100 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 5 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 1 TL = 100 cmv = 3 m/sR = 5 Ω

P = W

5.Hard

A long air-core solenoid has 1500 turns, a length of 50 cm and a diameter of 5 cm. Find its self-inductance L.

N = 1500l = 50 cm⌀ = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

L = mH

6.Hard

Two coils with self-inductances of 50 mH and 20 mH have a coupling coefficient of 0.3. The current in the first coil changes at 20 A/s. Find the emf ε induced in the second coil.

L₁ = 50 mHL₂ = 20 mHk = 0.3di/dt = 20 A/s

ε = V

Answer key

1. B = 31.42 µT
2. I = 4.001 A
3. B = 0.25 T
4. P = 1.8 W
5. L = 11.1 mH
6. ε = 0.1897 V

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