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 flat circular coil of 5 turns and radius 5 cm carries a current of 1 A. Find the magnetic flux density B at its centre.

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

B = µT

2.Easy

A solenoid 50 cm long has 2000 turns. Which current I gives a magnetic flux density of 12.57 mT inside it?

N = 2000L = 50 cmB = 12.57 mTμ₀ = 4π × 10⁻⁷ T·m/A

I = A

3.Medium

A coil of 20 turns has an area of 10 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.1 T, which is perpendicular to its plane, in 40 ms. Find the average induced emf ε.

N = 20A = 10 cm²B = 0.1 TΔt = 40 ms

ε = mV

4.Medium

A proton moves on a circle in a uniform magnetic field of 0.5 T. Find the time T it takes for one revolution.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CB = 0.5 T

T = ns

5.Hard

A long air-core solenoid has 200 turns, a length of 20 cm and a diameter of 1 cm. Find the energy W stored in its magnetic field when it carries 3 A.

N = 200l = 20 cm⌀ = 1 cmI = 3 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

6.Hard

A long air-core solenoid has 2000 turns, a length of 25 cm and a diameter of 2.5 cm. Find the energy W stored in its magnetic field when it carries 1 A.

N = 2000l = 25 cm⌀ = 2.5 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = mJ

Answer key

1. B = 62.83 µT
2. I = 2.501 A
3. ε = 100 mV
4. T = 131.2 ns
5. W = 88.83 µJ
6. W = 4.935 mJ

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