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 carries 4 A. How many turns N must it have for a flux density of 16.76 mT inside?

I = 4 AL = 30 cmB = 16.76 mTμ₀ = 4π × 10⁻⁷ T·m/A

N =

2.Easy

A straight wire 20 cm long lies at 90° to a uniform magnetic field of 0.12 T. The magnetic force on it is 0.072 N. Find the current I.

B = 0.12 TF = 0.072 NL = 20 cmθ = 90°

I = A

3.Medium

Two long parallel wires 12 cm apart carry currents of 30 A and 8 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 30 AI₂ = 8 Ad = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

A coil of 100 turns has an area of 40 cm². A uniform field perpendicular to the coil rises steadily from 0.1 T to 0.9 T in 20 ms. Find the average induced emf ε.

N = 100A = 40 cm²B: 0.1 T → 0.9 TΔt = 20 ms

ε = V

5.Hard

Two coils with self-inductances of 20 mH and 200 mH have a coupling coefficient of 0.9. The current in the first coil changes at 500 A/s. Find the emf ε induced in the second coil.

L₁ = 20 mHL₂ = 200 mHk = 0.9di/dt = 500 A/s

ε = V

6.Hard

In a velocity selector, crossed fields E = 2 × 10⁵ V/m and B = 0.05 T let only ions of one speed pass straight through. Find that speed v.

E = 2 × 10⁵ V/mB₁ = 0.05 T

v = m/s

Answer key

1. N = 1000
2. I = 3 A
3. F/L = 400 µN/m
4. ε = 16 V
5. ε = 28.46 V
6. v = 4 × 10⁶ m/s

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