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 100 turns and radius 12 cm carries a current of 2.5 A. Find the magnetic flux density B at its centre.

N = 100I = 2.5 AR = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

2.Easy

A rectangular loop of 20 cm by 20 cm lies in a uniform magnetic field of 0.1 T. The field makes an angle of 20° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.1 TA = 20 cm × 20 cm20° to the normal

Φ = mWb

3.Medium

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

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

F/L = µN/m

4.Medium

A metal rod 100 cm long slides at 1 m/s along two rails in a uniform field of 0.1 T into the page. Find the induced emf ε between its ends.

B = 0.1 TL = 100 cmv = 1 m/s

ε = mV

5.Hard

A short coil of 100 turns is wound tightly round the middle of a long solenoid of 800 turns, length 40 cm and diameter 2 cm. Find their mutual inductance M.

N₁ = 800N₂ = 100l = 40 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A

M = µH

6.Hard

A proton passes undeflected through a velocity selector with crossed fields E = 4 × 10⁴ V/m and B₁ = 0.05 T. It then enters a second region with only a magnetic field B₂ = 0.2 T, at right angles. Find the radius r of its path there.

E = 4 × 10⁴ V/mB₁ = 0.05 TB₂ = 0.2 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C

r = cm

Answer key

1. B = 1.309 mT
2. Φ = 3.759 mWb
3. F/L = 666.7 µN/m
4. ε = 100 mV
5. M = 78.96 µH
6. r = 4.177 cm

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