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 single circular loop of wire with radius 10 cm carries a current of 2 A. Find the magnetic flux density B at its centre.

N = 1I = 2 AR = 10 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A single circular loop of wire with radius 6 cm carries a current of 1.5 A. Find the magnetic flux density B at its centre.

N = 1I = 1.5 AR = 6 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

A coil of 100 turns has an area of 10 cm². The coil sits in a uniform field of 0.1 T perpendicular to its plane, and the field is switched off in 250 ms. Find the average induced emf ε.

N = 100A = 10 cm²B = 0.1 TΔt = 250 ms

ε = mV

4.Medium

An electron moves on a circle in a uniform magnetic field of 8 mT. Find the time T it takes for one revolution.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ CB = 8 mT

T = ns

5.Hard

A coil of 500 turns, 8 cm × 5 cm, rotates in a uniform field of 0.2 T about an axis perpendicular to the field. At what speed n (in revolutions per minute) must it turn to give an rms emf of 44.43 V?

N = 500A = 8 cm × 5 cmB = 0.2 TE_rms = 44.43 V

n = rpm

6.Hard

A deuteron passes undeflected through a velocity selector with crossed fields E = 5 × 10⁴ V/m and B₁ = 0.05 T. It then enters a second region with only a magnetic field B₂ = 0.2 T, at right angles. Find the radius r of its path there.

E = 5 × 10⁴ V/mB₁ = 0.05 TB₂ = 0.2 Tm = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C

r = cm

Answer key

1. B = 12.57 µT
2. B = 15.71 µT
3. ε = 40 mV
4. T = 4.466 ns
5. n = 1500 rpm
6. r = 10.44 cm

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