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 rectangular loop of 15 cm by 30 cm lies in a uniform magnetic field of 0.8 T. The field lines make an angle of 20° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.8 TA = 15 cm × 30 cm20° to the plane

Φ = mWb

2.Easy

A solenoid 40 cm long carries 2 A. How many turns N must it have for a flux density of 5.027 mT inside?

I = 2 AL = 40 cmB = 5.027 mTμ₀ = 4π × 10⁻⁷ T·m/A

N =

3.Medium

A proton moving at 5 × 10⁶ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 13.05 cm. Find the magnetic flux density B.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 5 × 10⁶ m/sr = 13.05 cm

B = T

4.Medium

An electron moves at 2 × 10⁶ m/s perpendicular to a uniform magnetic field of 8 mT. Find the radius r of its circular path.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 2 × 10⁶ m/sB = 8 mT

r = cm

5.Hard

Two coils with self-inductances of 50 mH and 200 mH have a coupling coefficient of 0.75. The current in the first coil changes at 50 A/s. Find the emf ε induced in the second coil.

L₁ = 50 mHL₂ = 200 mHk = 0.75di/dt = 50 A/s

ε = V

6.Hard

Two coils with self-inductances of 80 mH and 100 mH have a coupling coefficient of 0.3. The current in the first coil changes at 1000 A/s. Find the emf ε induced in the second coil.

L₁ = 80 mHL₂ = 100 mHk = 0.3di/dt = 1000 A/s

ε = V

Answer key

1. Φ = 12.31 mWb
2. N = 800.1
3. B = 0.4001 T
4. r = 0.1422 cm
5. ε = 3.75 V
6. ε = 26.83 V

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