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 solenoid 10 cm long has 250 turns and carries 0.5 A. Find the magnetic flux density B inside it, far from the ends.

N = 250L = 10 cmI = 0.5 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

2.Easy

A single circular loop of wire with radius 5 cm carries a current of 2 A. Find the magnetic flux density B at its centre.

N = 1I = 2 AR = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

3.Medium

An alpha particle moves on a circle in a uniform magnetic field of 0.2 T. Find the time T it takes for one revolution.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CB = 0.2 T

T = ns

4.Medium

An electron moving at 8 × 10⁶ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 0.5686 cm. Find the magnetic flux density B.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 8 × 10⁶ m/sr = 0.5686 cm

B = mT

5.Hard

A proton passes undeflected through a velocity selector with crossed fields E = 1 × 10⁴ V/m and B₁ = 0.4 T. It then enters a second region with only a magnetic field B₂ = 0.4 T, at right angles. Find the radius r of its path there.

E = 1 × 10⁴ V/mB₁ = 0.4 TB₂ = 0.4 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C

r = cm

6.Hard

A long air-core solenoid has 300 turns, a length of 10 cm and a diameter of 1.5 cm. Find the energy W stored in its magnetic field when it carries 0.5 A.

N = 300l = 10 cm⌀ = 1.5 cmI = 0.5 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

Answer key

1. B = 1.571 mT
2. B = 25.13 µT
3. T = 651.6 ns
4. B = 8 mT
5. r = 0.06527 cm
6. W = 24.98 µJ

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