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 12 cm by 10 cm lies in a uniform magnetic field of 1.2 T. The field makes an angle of 30° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 1.2 TA = 12 cm × 10 cm30° to the normal

Φ = mWb

2.Easy

A flat circular coil of 50 turns and radius 10 cm carries a current of 2.5 A. Find the magnetic flux density B at its centre.

N = 50I = 2.5 AR = 10 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

Two long parallel wires 12 cm apart carry currents of 30 A and 10 A in the same direction. Find the magnitude of the magnetic flux density B at point P, halfway between them.

I₁ = 30 AI₂ = 10 Ad = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

4.Medium

A coil of 50 turns has an area of 200 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.4 T, which is perpendicular to its plane, in 250 ms. Find the average induced emf ε.

N = 50A = 200 cm²B = 0.4 TΔt = 250 ms

ε = V

5.Hard

A long air-core solenoid has 100 turns, a length of 15 cm and a diameter of 3 cm. Find its self-inductance L.

N = 100l = 15 cm⌀ = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A

L = µH

6.Hard

A coil of 200 turns, 12 cm × 25 cm, rotates at 600 rpm in a uniform field of 0.2 T about an axis perpendicular to the field. Find the peak emf E₀.

N = 200A = 12 cm × 25 cmB = 0.2 Tn = 600 rpm

E₀ = V

Answer key

1. Φ = 12.47 mWb
2. B = 785.4 µT
3. B = 66.67 µT
4. ε = 3.2 V
5. L = 59.22 µH
6. E₀ = 75.4 V

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