Physics 1B: Magnetism & Electromagnetic Induction

Magnets and magnetic fields

A magnet is any object with a persistent magnetic field. Every magnet has a north pole and a south pole. Like poles repel; unlike poles attract — the same qualitative rule you saw for charges. The important difference: magnetic monopoles do not exist. You can never separate a magnet's north from its south. Cut a bar magnet in half and each piece becomes a smaller bar magnet with its own north and south. This is a deep and testable fact about how nature is structured.

A magnetic field (symbol B) is the region around a magnet where another magnet, or a moving charge, would experience a force. The SI unit is the tesla (T). Earth's magnetic field, which orients compass needles, is about 5 × 10⁻⁵ T — quite weak. A refrigerator magnet is about 5 × 10⁻³ T. An MRI machine reaches roughly 1.5 T.

Force on a moving charge

A magnetic field exerts a force ONLY on charges that are moving. A stationary charge in a magnetic field feels nothing. The magnitude of the force on a moving charge is:

F = q · v · B · sin θ

Where q is the charge magnitude, v is the speed, B is the magnetic field strength, and θ is the angle between the velocity and the field. Two consequences:

• If the charge moves parallel to the field (θ = 0° or 180°), sin θ = 0, so F = 0. No force.
• If the charge moves perpendicular to the field (θ = 90°), sin θ = 1, so F is maximum: F = qvB.

Force direction is given by the right-hand rule: for a positive charge, point your fingers in the direction of velocity, curl them toward the direction of B, and your thumb points in the direction of the force. For a negative charge, reverse it.

A striking consequence: the force is always perpendicular to the velocity. Perpendicular force means no work is done (W = Fd cos 90° = 0). So a magnetic field can change the direction of a charged particle's motion, but never its speed. Charged particles in a uniform magnetic field move in circles — this is the principle behind particle accelerators like cyclotrons.

Force on a current-carrying wire

A wire carrying current is just a collection of moving charges. When the wire sits in a magnetic field, all those charges feel forces, which add up to a net force on the wire:

F = B · I · L · sin θ

Where I is the current, L is the length of wire in the field, and θ is the angle between the current direction and B. This is what makes electric motors work: put current-carrying wire loops in a magnetic field, and the resulting forces spin the loops.

Electromagnetic induction — the reverse trick

Here is one of the most surprising and consequential discoveries in physics, made independently by Michael Faraday and Joseph Henry in 1831: a changing magnetic field induces an electric current in a nearby conductor. Not a static magnetic field — a CHANGING one.

The formal statement is Faraday's law of induction. In qualitative terms:

The induced EMF is proportional to the rate at which the magnetic flux changes.

Magnetic flux (Φ) through a loop is a measure of how many field lines pass through it. Flux changes when the field strength changes, when the loop area changes, or when the angle between the loop and the field changes. Any of the three will induce a current.

This principle is why:

• Moving a bar magnet toward or away from a coil generates a current in the coil (the changing flux induces EMF).
• Rotating a coil in a magnetic field generates alternating current — this is the operating principle of every electrical generator, from a hand-crank flashlight to a hydroelectric dam.
• An alternating current in one coil creates a changing magnetic field, which induces current in a nearby coil — the operating principle of a transformer.

Transformers — stepping voltages up and down

A transformer uses electromagnetic induction to convert alternating voltage from one level to another. Two coils share an iron core: the "primary" coil is driven by an AC source, its alternating field induces a voltage in the "secondary" coil. The voltage ratio depends on the ratio of the number of turns in each coil:

V_p / V_s = N_p / N_s

Where V_p and V_s are primary and secondary voltages, and N_p and N_s are the number of turns of wire. A transformer with 100 turns on the primary and 1000 on the secondary steps voltage UP by a factor of 10. This is called a step-up transformer. Reversed, it becomes a step-down transformer.

Idealized transformers are 100% efficient (real ones are 95-98%), so power is conserved: V_p·I_p = V_s·I_s. A step-up transformer that multiplies voltage by 10 divides current by 10. This is why long-distance power transmission uses very high voltage: high V means low I, and resistive losses go as I²R. Local substations then step voltage back down for residential use.

Lenz's law — the direction of induced currents

Faraday's law tells you the magnitude of induced EMF; Lenz's law tells you its direction. The rule: the induced current always flows in whatever direction opposes the change in flux that caused it. This is another example of energy conservation. If the change did not oppose itself, you could get free energy — which is not how nature works.

Everyday example: push a bar magnet toward a coil, and the induced current in the coil creates a magnetic field that pushes back on your incoming magnet. To keep it moving toward the coil, you have to do work — that work goes into the electrical energy being generated. Free energy is off the table.

Motors and generators — related opposites

An electric motor converts electrical energy into mechanical energy. Current flows through wire loops in a magnetic field; the resulting forces make the loops spin. That spinning is the useful output.

An electric generator does the reverse. Mechanical input spins wire loops through a magnetic field; the resulting changing flux induces current in the loops. That current is the useful output.

The two devices are physically identical: same coils, same magnets, same shaft. Only the direction of energy flow differs. A moving car's engine can drive its wheels; a car pushed downhill turns those same wheels which can drive an alternator that recharges the battery. Any motor can act as a generator, and vice versa.

Where students lose points

• Assuming magnetic force acts on stationary charges. It does not. Only moving charges feel magnetic forces.
• Confusing electric field with magnetic field. Both are vector fields, but they act on different quantities (E on any charge, B only on moving charges).
• Applying transformer formula to DC. Transformers require CHANGING flux. DC (constant current) produces no changing field, so no induction and no voltage transformation. This is why the electric grid uses AC.
• Using left-hand rule instead of right-hand rule for positive charges. The convention is right-hand for positive charges; left-hand only for negative charges.
• Forgetting that induced current opposes the change. Lenz's law means every induced-current question requires a mental "what direction would push back on the change" step.

Worked example — transformer ratio

A transformer has 200 turns on the primary coil and 800 turns on the secondary coil. If 120 V AC is applied to the primary, what is the secondary voltage?

Step 1 — Apply the transformer equation: V_s = V_p × (N_s / N_p).

Step 2 — Plug in: V_s = 120 × (800/200) = 120 × 4 = 480 V.

This is a step-up transformer with a 4× voltage boost. Correspondingly, if you know the current on the primary side, current on the secondary side will be 4× smaller (power conservation).

Check yourself

1. State the rule for like and unlike magnetic poles.
2. Why does a stationary charge feel no force in a magnetic field?
3. State Faraday's law of induction in your own words.
4. Explain why transformers require AC current to function.
5. What is the fundamental relationship between generators and motors?
6. A transformer has V_p = 240 V, N_p = 100 turns, and N_s = 25 turns. Find V_s and identify whether it is step-up or step-down.

(Answer to #6: V_s = 240 × (25/100) = 60 V. Step-down transformer.)

Practice with CBE-style questions

Magnetism and induction problems on the CBE often combine concepts — motion of charges, force on wires, and changing flux — with straightforward numerical setups. Work through the practice bank filtered by Magnetism & Electromagnetic Induction for questions with step-by-step solutions.

Independent practice content aligned to Texas Essential Knowledge and Skills (TEKS) §112.39(c)(5)(G). Not affiliated with TTU K-12, UT High School, UT-Austin, the Texas Education Agency, or any Credit by Examination administrator. Texas CBE™ does not administer any exam or grant academic credit.