Magnetism: study guide

Key ideas

Magnetic fields are made by moving charges and act on moving charges. The force is always perpendicular to both the field and the velocity, so it changes the direction of motion but not the speed.

• The force on a charge is F = qvB sin θ, and on a wire F = BIL sin θ. It is zero when the motion is along the field.
• A charged particle moving perpendicular to a uniform field travels in a circle of radius r = mv ÷ (qB).
• A long straight wire makes a field B = μ₀I ÷ (2πr), and a solenoid has B = μ₀nI inside, where n is turns per meter.
• Two parallel wires attract if the currents run the same way and repel if they run opposite ways.

Key equations

• F = qvB sin θ
• F = BIL sin θ
• B = μ₀I ÷ (2πr)
• B = μ₀nI (solenoid)
• r = mv ÷ (qB)
• F ÷ L = μ₀I₁I₂ ÷ (2πd)
• Φ = BA cos θ

Worked example

A proton (q = 1.6 × 10⁻¹⁹ C, m = 1.67 × 10⁻²⁷ kg) moves at 1.0 × 10⁶ m/s perpendicular to a field of 0.10 T. F = qvB = 1.6 × 10⁻¹⁹ × 1.0 × 10⁶ × 0.10 = 1.6 × 10⁻¹⁴ N. The radius is r = mv ÷ (qB) = 1.67 × 10⁻²⁷ × 1.0 × 10⁶ ÷ (1.6 × 10⁻¹⁹ × 0.10) = 0.10 m.

Common mistakes

• Expecting a force on a charge that moves along the field direction. The force is zero there.
• Forgetting to flip the direction for a negative charge when using the right-hand rule.
• Thinking the magnetic force speeds the particle up. It does no work, so the speed stays constant.

Practice

Test yourself with practice questions on this topic: Magnetism