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 30 cm long has 1000 turns and carries 5 A. Find the magnetic flux density B inside it, far from the ends.

N = 1000L = 30 cmI = 5 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

2.Easy

A straight wire 80 cm long carries 4 A at an angle of 60° to a uniform magnetic field of 1.2 T. Find the magnitude of the force F on the wire.

B = 1.2 TI = 4 AL = 80 cmθ = 60°

F = N

3.Medium

An alpha particle moves on a circle in a uniform magnetic field of 1 T. Find the time T it takes for one revolution.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CB = 1 T

T = ns

4.Medium

Two long parallel wires 5 cm apart carry currents of 20 A and 12 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 20 AI₂ = 12 Ad = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

5.Hard

An alpha particle starts from rest, is accelerated through a potential difference of 1000 V and then enters a uniform magnetic field of 0.4 T at right angles. Find the radius r of its path in the field.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CV = 1000 VB = 0.4 T

r = cm

6.Hard

A short coil of 200 turns is wound tightly round the middle of a long solenoid of 1500 turns, length 30 cm and diameter 3 cm. Find their mutual inductance M.

N₁ = 1500N₂ = 200l = 30 cm⌀ = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A

M = µH

Answer key

1. B = 20.94 mT
2. F = 3.326 N
3. T = 130.3 ns
4. F/L = 960 µN/m
5. r = 1.61 cm
6. M = 888.3 µH

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