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 10 cm by 30 cm lies in a uniform magnetic field of 0.5 T. The field makes an angle of 20° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.5 TA = 10 cm × 30 cm20° to the normal

Φ = mWb

2.Easy

A rectangular loop of 10 cm by 25 cm lies in a uniform magnetic field of 0.4 T. The field lines make an angle of 53° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.4 TA = 10 cm × 25 cm53° to the plane

Φ = mWb

3.Medium

Two long parallel wires 20 cm apart carry currents of 5 A and 12 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 5 AI₂ = 12 Ad = 20 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

A proton moves at 2.5 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.1 T. Find the radius r of its circular path.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 2.5 × 10⁶ m/sB = 0.1 T

r = cm

5.Hard

A coil of 200 turns, 10 cm × 25 cm, rotates at 300 rpm in a uniform field of 0.1 T about an axis perpendicular to the field. Find the peak emf E₀.

N = 200A = 10 cm × 25 cmB = 0.1 Tn = 300 rpm

E₀ = 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 0.5 A.

N = 2000l = 15 cm⌀ = 2 cmI = 0.5 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = mJ

Answer key

1. Φ = 14.1 mWb
2. Φ = 7.986 mWb
3. F/L = 60 µN/m
4. r = 26.11 cm
5. E₀ = 15.71 V
6. W = 1.316 mJ

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