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

An alpha particle moves at 5 × 10⁶ m/s at an angle of 30° to a uniform magnetic field of 1.5 T. Find the magnitude of the magnetic force F on it.

|q| = 3.204 × 10⁻¹⁹ Cv = 5 × 10⁶ m/sB = 1.5 Tθ = 30°

F = pN

2.Easy

A solenoid 20 cm long has 1000 turns. Which current I gives a magnetic flux density of 31.42 mT inside it?

N = 1000L = 20 cmB = 31.42 mTμ₀ = 4π × 10⁻⁷ T·m/A

I = A

3.Medium

A coil of 10 turns has an area of 50 cm². The coil sits in a uniform field of 0.8 T perpendicular to its plane, and the field is switched off in 20 ms. Find the average induced emf ε.

N = 10A = 50 cm²B = 0.8 TΔt = 20 ms

ε = V

4.Medium

An alpha particle moves at 1 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.5 T. Find the radius r of its circular path.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 1 × 10⁵ m/sB = 0.5 T

r = cm

5.Hard

A short coil of 50 turns is wound tightly round the middle of a long solenoid of 1500 turns, length 20 cm and diameter 4 cm. Find their mutual inductance M.

N₁ = 1500N₂ = 50l = 20 cm⌀ = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A

M = µH

6.Hard

A proton passes undeflected through a velocity selector with crossed fields E = 5 × 10⁴ V/m and B₁ = 0.4 T. It then enters a second region with only a magnetic field B₂ = 0.25 T, at right angles. Find the radius r of its path there.

E = 5 × 10⁴ V/mB₁ = 0.4 TB₂ = 0.25 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C

r = cm

Answer key

1. F = 1.202 pN
2. I = 5.001 A
3. ε = 2 V
4. r = 0.4148 cm
5. M = 592.2 µH
6. r = 0.5222 cm

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