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

The magnetic flux density 12 cm from a long straight wire is 16.67 µT. Find the current I in the wire.

B = 16.67 µTr = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A

I = A

2.Easy

A solenoid 40 cm long has 1000 turns and carries 4 A. Find the magnetic flux density B inside it, far from the ends.

N = 1000L = 40 cmI = 4 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

3.Medium

Two long parallel wires 4 cm apart carry currents of 30 A and 15 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 30 AI₂ = 15 Ad = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

An alpha particle moving at 1.5 × 10⁶ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 31.11 cm. Find the magnetic flux density B.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 1.5 × 10⁶ m/sr = 31.11 cm

B = T

5.Hard

A long air-core solenoid has 500 turns, a length of 20 cm and a diameter of 4 cm. Find the energy W stored in its magnetic field when it carries 1.5 A.

N = 500l = 20 cm⌀ = 4 cmI = 1.5 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = mJ

6.Hard

A short coil of 200 turns is wound tightly round the middle of a long solenoid of 800 turns, length 50 cm and diameter 2 cm. The current in the solenoid changes at 1000 A/s. Find the emf ε induced in the short coil.

N₁ = 800N₂ = 200l = 50 cm⌀ = 2 cmdi/dt = 1000 A/sμ₀ = 4π × 10⁻⁷ T·m/A

ε = mV

Answer key

1. I = 10 A
2. B = 12.57 mT
3. F/L = 2250 µN/m
4. B = 0.1 T
5. W = 2.221 mJ
6. ε = 126.3 mV

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