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Physics 2 Unit 4: Magnetism and electromagnetism

Moving charges create magnetic fields and feel magnetic forces, and changing magnetic flux induces voltage.

Covers: Magnetic fields, magnetic force on moving charges and wires, fields of currents, magnetic flux, Faraday's and Lenz's laws, induced emf, electromagnetic applications

Study guide

Magnets have north and south poles; like poles repel, and magnetic poles always come in pairs. Magnetic field lines go from north to south outside a magnet. Earth has a magnetic field, and ferromagnetic materials like iron have magnetic domains that can align. Magnetic fields are measured in teslas (T). A charge moving through a magnetic field feels a force F = qvB sin θ, perpendicular to both the velocity and the field, given by the right-hand rule (reversed for negative charges). Because the force is perpendicular to the velocity, it does no work and doesn't change the particle's speed; a charge moving perpendicular to a uniform field travels in a circle of radius r = mv/(qB).

A current-carrying wire in a magnetic field feels a force F = ILB sin θ, which is how electric motors work. Moving charges and currents create magnetic fields. A long straight wire creates circular field lines around it, with strength B = μ₀I/(2πr), and the direction comes from another right-hand rule: thumb along the current, fingers curl with the field. Two parallel wires with currents in the same direction attract; opposite currents repel. A solenoid (coil) creates a nearly uniform field inside, acting like a bar magnet, the basis of electromagnets.

Magnetic flux is the amount of field passing through an area: ΦB = BA cos θ. Faraday's law says a changing magnetic flux induces an emf: ε = −N(ΔΦB/Δt). Flux can change because the field changes, the area changes or the loop rotates. A conducting rod moving through a field has motional emf ε = BLv. Lenz's law gives the direction: the induced current creates a magnetic field that opposes the change in flux, which is the reason for the negative sign. Electromagnetic induction powers generators, which turn mechanical energy into electrical energy, and transformers, which change AC voltages. It's also used in induction cooktops, wireless chargers and credit card readers.

When perpendicular electric and magnetic fields both act on a moving charge, the forces cancel only if qE = qvB. Only particles with speed v = E/B pass straight through, whatever their charge or mass. Between parallel plates E = ΔV/d, so v = ΔV/(Bd). Two long parallel wires a distance d apart exert forces on each other of F/L = μ₀I₁I₂/(2πd). The force is attractive when the currents flow the same way and repulsive when they flow opposite ways. Each wire's force on the other is equal and opposite.

Bar magnets, current loops and even electrons act as magnetic dipoles. Magnetic field lines form closed loops, running from north to south outside a magnet and from south to north inside it. A compass needle is a small dipole that lines up with the local magnetic field.

Key ideas

• Magnetic force on a moving charge is perpendicular to velocity and field.
• Magnetic forces do no work on charges.
• Currents create magnetic fields; parallel currents in the same direction attract.
• Changing magnetic flux induces an emf (Faraday's law).
• Lenz's law: induced current opposes the change in flux.

Formulas and rules

Common mistakes

• Thinking a magnetic field can speed up a charge; it only changes direction.
• Thinking a constant flux induces emf; only a changing flux does.

Words to know

Magnetic field

A region where magnetic forces act.

Tesla

The SI unit of magnetic field.

Magnetic domain

A region in which atomic magnetic fields align.

Right-hand rule

A method for finding the direction of magnetic force or field.

Magnetic force on a charge

F = qvB sin θ.

Magnetic force on a wire

F = ILB sin θ.

Electric motor

A device that uses magnetic force on currents to create motion.

Solenoid

A coil of wire that creates a uniform field inside.

Electromagnet

A magnet created by electric current.

Magnetic flux

The amount of magnetic field through an area.

Faraday's law

A changing magnetic flux induces an emf.

Lenz's law

Induced current opposes the change in flux.

Induced emf

Voltage produced by a changing magnetic flux.

Motional emf

emf from a conductor moving through a magnetic field.

Generator

A device that converts mechanical energy into electrical energy.

Transformer

A device that changes AC voltage using induction.

Sample practice questions

5 more questions like these, from level 1 to 5, are in the practice set.