12.3 Magnetism and Electromagnetic Induction

Magnetism Fundamentals

Magnetism and electromagnetic induction explain how magnetic fields and electric currents influence each other. This relationship is the foundation for technologies like electric motors, generators, and transformers, and it connects directly to how electromagnetic waves work.

Magnetic Fields and Poles

A magnetic field is the region around a magnet where it exerts force on other magnets or magnetic materials. You can visualize it using magnetic field lines.

• Field lines show both the direction and strength of the field
  • Lines packed close together mean a stronger field
  • Lines spread far apart mean a weaker field
• Field lines always form closed loops (exiting the north pole, curving around, and entering the south pole). They never cross each other.

Magnets always have two poles, north and south, and you can't isolate one from the other. If you break a magnet in half, you get two smaller magnets, each with its own north and south pole.

• Like poles repel (north-north or south-south push apart)
• Unlike poles attract (north-south pull together)

Earth itself behaves like a giant magnet. Its magnetic poles sit near (but not exactly at) the geographic poles. That's why a compass needle, which is a small magnet free to rotate, aligns roughly north-south.

Electromagnets and Solenoids

An electromagnet creates a magnetic field using electric current rather than a permanent magnet. The basic setup is a coil of wire wrapped around a ferromagnetic core (usually iron). Two things increase the field strength: more current and more turns of wire.

A solenoid is a specific type of electromagnet: a long, tightly wound coil. When current flows through it, the solenoid produces a nearly uniform magnetic field inside the coil. The field strength inside is given by:

$B = \mu_0 n I$

• $B$: magnetic field strength (in teslas, T)
• $\mu_0$: permeability of free space ($4\pi \times 10^{-7}$ T·m/A)
• $n$: number of turns per unit length (turns/meter)
• $I$: current through the solenoid (in amps)

So if you double the current, you double the field strength. Same goes for doubling the turn density.

Common applications of electromagnets include electric motors, loudspeakers, and MRI machines.

Electromagnetic Induction

Faraday's Law and Induced Current

Electromagnetic induction is the process of generating an electric current by changing the magnetic field through a loop of wire. This is the principle behind generators and transformers.

Faraday's law says the induced electromotive force (EMF) in a closed loop equals the negative rate of change of magnetic flux through that loop:

$\varepsilon = -N \frac{\Delta \Phi}{\Delta t}$

• $\varepsilon$: induced EMF (in volts)
• $N$: number of turns in the coil
• $\Delta \Phi$: change in magnetic flux (in webers, Wb)
• $\Delta t$: time interval over which the change occurs

Magnetic flux ($\Phi$) depends on the magnetic field strength, the area of the loop, and the angle between the field and the loop. So you can induce an EMF by changing any of those three things: move a magnet closer, change the loop's area, or rotate the loop in the field.

The negative sign comes from Lenz's law, which states that the induced current flows in whatever direction opposes the change that caused it. For example, if you push a magnet's north pole toward a coil, the induced current creates its own north pole facing the magnet, resisting the approach. This isn't arbitrary; it's a direct consequence of conservation of energy. If the induced current helped the change instead of opposing it, you'd get energy from nothing.

Generators and Transformers

Generators convert mechanical energy into electrical energy using electromagnetic induction. Here's how they work:

1. A coil of wire rotates inside a magnetic field (or a magnet rotates around a coil).
2. As the coil turns, the magnetic flux through it constantly changes.
3. By Faraday's law, this changing flux induces an EMF in the coil.
4. The EMF drives current through an external circuit.

• AC generators produce alternating current because the coil's rotation causes the induced voltage to rise and fall in a sinusoidal pattern.
• DC generators add a commutator (a split-ring connector) that flips the output connections every half-turn, keeping the current flowing in one direction.

Transformers change AC voltage from one level to another. They only work with AC because they rely on a changing magnetic field.

1. Current in the primary coil creates a changing magnetic field in a shared iron core.
2. That changing field passes through the secondary coil.
3. By Faraday's law, the secondary coil experiences an induced EMF.

The voltage ratio between the two coils is set by the turn ratio:

$\frac{V_p}{V_s} = \frac{N_p}{N_s}$

• $V_p$, $V_s$: primary and secondary voltages
• $N_p$, $N_s$: number of turns in primary and secondary coils

If the secondary coil has more turns than the primary, voltage goes up (step-up transformer). If it has fewer turns, voltage goes down (step-down transformer). In an ideal transformer, power is conserved, so stepping up voltage means stepping down current, and vice versa.

Electromagnetic Spectrum

Properties and Types of Electromagnetic Waves

All electromagnetic (EM) waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction the wave travels. Unlike sound waves, EM waves don't need a medium; they can travel through a vacuum.

Every EM wave travels at the speed of light in a vacuum:

$c \approx 3 \times 10^8 \text{ m/s}$

Wavelength, frequency, and the speed of light are related by:

$c = \lambda f$

• $\lambda$: wavelength (in meters)
• $f$: frequency (in hertz, Hz)

This means wavelength and frequency are inversely related. Longer wavelength means lower frequency, and shorter wavelength means higher frequency.

The electromagnetic spectrum organizes all EM radiation from longest wavelength to shortest:

As you move from radio waves toward gamma rays, wavelength decreases, frequency increases, and the energy carried by each photon increases. That's why gamma rays and X-rays can be dangerous: their high energy can damage cells and DNA.