Unit 12 · Magnetism and Electromagnetism

Magnetic field ● (core concept) — A vector field that determines the magnetic force on moving charges, currents, and magnetic materials. It can be drawn as a vector field map.

Magnetic dipole ● (core concept) — The fundamental source of magnetic fields: circular or rotational motion of electric charges. Dipoles have north and south poles; there are no magnetic monopoles — breaking a bar magnet yields two dipoles, never an isolated pole.

Magnetic field lines ● (core concept) — Field lines that always form closed loops. Outside a bar magnet they leave the north pole and return to the south pole. Like poles repel, opposite poles attract.

Ferromagnetic material ● (core concept) — A material (iron, nickel, cobalt) that can be permanently magnetized because an external field aligns its magnetic domains or atomic dipoles, and the alignment persists after the field is removed.

Paramagnetic material ○ — A material (aluminum, titanium, magnesium) whose dipoles align weakly with an external field but lose the alignment when the field is removed.

Diamagnetic material ○ — All materials show diamagnetism: their electron structure creates a weak dipole alignment opposite the external field.

Magnetic permeability ● (core concept) — A measure of how much a material magnetizes in response to an external magnetic field. Free space has the constant value μ₀ = 4π×10⁻⁷ (T·m)/A; matter's permeability differs and varies with temperature, orientation, and field strength.

Magnetic domain ● (core concept) — A microscopic region within a ferromagnetic material whose atomic dipoles are aligned. An external field aligns the domains, magnetizing the material; in a permanent magnet the alignment persists.

Magnetic field of a moving charge ● (core concept) — A moving charged object produces a magnetic field whose direction is perpendicular to both the velocity and the position vector from the object, found with the right-hand rule. Its magnitude is largest when velocity and position vector are perpendicular.

Magnetic force on a moving charge ● (core concept) — F_B = qvB sinθ: proportional to the charge, its speed, and the field strength, and dependent on the angle between velocity and field. Quantitative treatment is limited to θ = 0°, 90°, and 180°. Direction (right-hand rule) is perpendicular to both v and B; it does no work since it is always perpendicular to the velocity.

Hall effect ● (core concept) — The potential difference created across a conductor when a magnetic field with a component perpendicular to the moving charges deflects them to one side of the conductor.

Right-hand rule (magnetism) ○ — The hand rule giving magnetic directions: thumb along a wire's current, curled fingers along the field around it; for a moving charge, fingers along v then curled toward B give the force direction on a positive charge. The force is always perpendicular to both the velocity (or current) and the field.

Magnetic field of a current-carrying wire ● (core concept) — B = μ₀I/(2πr): the field a perpendicular distance r from a long straight wire is proportional to the current and inversely proportional to the distance. Field vectors form concentric circles around the wire, with direction given by the right-hand rule (thumb along current, fingers curl along B).

Magnetic field at the center of a current loop ● (core concept) — Directed along the loop's axis, with the sense given by the right-hand rule (fingers curl with the current, thumb points along the field).

Magnetic force on a current-carrying wire ● (core concept) — F_B = IℓB sinθ: proportional to the current, the length of wire in the field, and the field strength, and dependent on the angle between the current direction and the field. Direction from the right-hand rule.

Magnetic flux ● (core concept) — Φ_B = |B|cosθ|A|: the component of the magnetic field perpendicular to a surface times the surface's area. The sign is positive when B is parallel to the area vector (defined perpendicular to the surface, outward from a closed surface) and negative when antiparallel.

Faraday's law ● (core concept) — A changing magnetic flux induces an emf: |ε| = |ΔΦ_B/Δt|, or ε = −NΔΦ_B/Δt for a coil of N turns. Only the rate of change of flux matters — a steady flux induces nothing.

Lenz's law ● (core concept) — The direction of an induced emf (and its current) always opposes the change in magnetic flux that produced it — the physical content of the minus sign in Faraday's law. Use the right-hand rule to relate the induced current's field to the flux change.

Motional emf ● (core concept) — ε = Bℓv: the emf induced in a conductor of length ℓ moving with speed v perpendicular to a uniform magnetic field B — e.g., a rod sliding on conducting rails. A derived consequence of Faraday's law.

Induced current ● (core concept) — The current driven in a conductor by an induced emf. Its direction, given by Lenz's law, always opposes the change in magnetic flux that produced it.