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 6 cm carries a current of 4 A. Find the magnetic flux density B at its centre.

N = 100I = 4 AR = 6 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

2.Easy

A straight wire 15 cm long lies at 60° to a uniform magnetic field of 0.25 T. The magnetic force on it is 0.2598 N. Find the current I.

B = 0.25 TF = 0.2598 NL = 15 cmθ = 60°

I = A

3.Medium

A coil of 500 turns, area 50 cm² and resistance 20 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.25 T in 50 ms. Find the average induced current I.

N = 500A = 50 cm²B: 0.05 T → 0.25 TΔt = 50 msR = 20 Ω

I = mA

4.Medium

Two long parallel wires 8 cm apart carry currents of 5 A and 10 A in opposite directions. Find the force per metre of length F/L between them.

I₁ = 5 AI₂ = 10 Ad = 8 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

5.Hard

A long air-core solenoid has 400 turns, a length of 40 cm and a diameter of 4 cm. Find the energy W stored in its magnetic field when it carries 4 A.

N = 400l = 40 cm⌀ = 4 cmI = 4 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = mJ

6.Hard

In a velocity selector, crossed fields E = 5 × 10⁴ V/m and B = 0.5 T let only ions of one speed pass straight through. Find that speed v.

E = 5 × 10⁴ V/mB₁ = 0.5 T

v = m/s

Answer key

1. B = 4.189 mT
2. I = 8 A
3. I = 500 mA
4. F/L = 125 µN/m
5. W = 5.053 mJ
6. v = 100000 m/s

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