Magnetism
Easy Overview
Ever played with a compass and noticed how it always points north? That's Earth's magnetic field at work. This chapter is about magnetic fields — how they're created by electric currents, how they affect moving charges, and why some materials are magnetic while others aren't. It's the physics behind electric motors, MRI machines, and your phone's speaker.
Magnetic Field and Lorentz Force
Magnetic fields (B) are regions where moving charges experience force. The Lorentz force on a charge q moving with velocity v in magnetic field B is F = q(v × B) — it's a cross product, so the force is perpendicular to both v and B. That means magnetic force does NO work (it changes direction, not speed). The unit is tesla (T). Earth's magnetic field is about 5×10⁻⁵ T. A fridge magnet is about 0.01 T.
Biot-Savart Law — How Currents Make Fields
The Biot-Savart law tells you the magnetic field produced by a small segment of current-carrying wire. dB = (μ₀/4π) × (Idl × r̂)/r². μ₀ = 4π×10⁻⁷ T·m/A is the permeability of free space. For a long straight wire: B = μ₀I/(2πr) — field circles around the wire. Right-hand thumb rule: thumb points in current direction, fingers curl in field direction.
Ampere's Circuital Law
Ampere's law is like Gauss's law for magnetism: ∮ B·dl = μ₀I_enclosed. The line integral of the magnetic field around a closed loop equals μ₀ times the current passing through the loop. It's a shortcut for calculating B in symmetrical situations. For a long solenoid (a coil of wire): B = μ₀nI, where n is the number of turns per meter. Solenoids are used as electromagnets.
Force Between Current-Carrying Wires
Two parallel wires carrying current attract if currents are in the same direction, repel if opposite. The force per unit length: F/L = μ₀I₁I₂/(2πd). This is because each wire creates a magnetic field that affects the other. This is the definition of the ampere — 1 A is the current that produces a force of 2×10⁻⁷ N/m between two parallel wires 1 m apart.
Magnetic Materials — Dia, Para, and Ferro
Diamagnetic materials (copper, bismuth) are weakly repelled by magnets — all materials have this. Paramagnetic materials (aluminum, oxygen) are weakly attracted. Ferromagnetic materials (iron, nickel, cobalt) are strongly attracted and can become permanent magnets. Ferromagnetic materials have domains — regions where atomic magnetic moments align. When you magnetize iron, all domains align in the same direction. Curie temperature: above this, ferromagnetic materials become paramagnetic.
Key Points
- •Lorentz force: F = q(v × B) — force perpendicular to velocity and field
- •Right-hand thumb rule: current → thumb, field → curled fingers
- •Biot-Savart law: dB ∝ Idl × r̂ / r²
- •Ampere's law: ∮ B·dl = μ₀I_enclosed
- •Solenoid: B = μ₀nI (uniform field inside)
- •Force between parallel wires: F/L = μ₀I₁I₂/(2πd)
- •Ferromagnetic materials have domains that align to become magnets
Practice Questions
- A long straight wire carries 5 A current. Find the magnetic field at a distance of 10 cm from the wire.
- State and explain the Biot-Savart law. Use it to find B at the center of a circular current loop.
- Derive the expression for force between two parallel current-carrying conductors.
- Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials.