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 25 cm lies in a uniform magnetic field of 0.8 T. The field makes an angle of 53° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.8 TA = 5 cm × 25 cm53° to the normal

Φ = mWb

2.Easy

A rectangular loop of 10 cm by 10 cm lies in a uniform magnetic field of 0.25 T. The field makes an angle of 37° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.25 TA = 10 cm × 10 cm37° to the normal

Φ = mWb

3.Medium

An electron moves on a circle in a uniform magnetic field of 5 mT. Find the time T it takes for one revolution.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ CB = 5 mT

T = ns

4.Medium

A coil of 20 turns has an area of 25 cm². The coil sits in a uniform field of 0.1 T perpendicular to its plane, and the field is switched off in 500 ms. Find the average induced emf ε.

N = 20A = 25 cm²B = 0.1 TΔt = 500 ms

ε = mV

5.Hard

A long air-core solenoid has 800 turns, a length of 15 cm and a diameter of 1.5 cm. Find its self-inductance L.

N = 800l = 15 cm⌀ = 1.5 cmμ₀ = 4π × 10⁻⁷ T·m/A

L = µH

6.Hard

A coil of 200 turns, 15 cm × 15 cm, rotates at 1800 rpm in a uniform field of 0.25 T about an axis perpendicular to the field. Find the rms value E_rms of the emf.

N = 200A = 15 cm × 15 cmB = 0.25 Tn = 1800 rpm

E_rms = V

Answer key

1. Φ = 6.018 mWb
2. Φ = 1.997 mWb
3. T = 7.145 ns
4. ε = 10 mV
5. L = 947.5 µH
6. E_rms = 149.9 V

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