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 5 cm by 20 cm lies in a uniform magnetic field of 0.2 T. The field makes an angle of 30° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.2 TA = 5 cm × 20 cm30° to the normal

Φ = mWb

2.Easy

A solenoid 15 cm long has 2000 turns. Which current I gives a magnetic flux density of 33.51 mT inside it?

N = 2000L = 15 cmB = 33.51 mTμ₀ = 4π × 10⁻⁷ T·m/A

I = A

3.Medium

An alpha particle moves at 5 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.1 T. Find the radius r of its circular path.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 5 × 10⁵ m/sB = 0.1 T

r = cm

4.Medium

A proton moving at 6 × 10⁵ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 2.506 cm. Find the magnetic flux density B.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 6 × 10⁵ m/sr = 2.506 cm

B = T

5.Hard

A coil of 250 turns, 12 cm × 25 cm, rotates at 1200 rpm in a uniform field of 0.3 T about an axis perpendicular to the field. Find the rms value E_rms of the emf.

N = 250A = 12 cm × 25 cmB = 0.3 Tn = 1200 rpm

E_rms = V

6.Hard

A coil of 20 turns, 12 cm × 5 cm, rotates at 3000 rpm in a uniform field of 0.3 T about an axis perpendicular to the field. Find the peak emf E₀.

N = 20A = 12 cm × 5 cmB = 0.3 Tn = 3000 rpm

E₀ = V

Answer key

1. Φ = 1.732 mWb
2. I = 2 A
3. r = 10.37 cm
4. B = 0.25 T
5. E_rms = 199.9 V
6. E₀ = 11.31 V

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