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Magnetism and ElectromagnetismπŸ”—

Beginner

This article is in the Circuit Foundations topic. It builds on Current and AC vs DC. No other prior knowledge required.

Wrap insulated wire around an ordinary steel nail, connect the two ends to a battery, and the nail picks up paper clips. Disconnect the battery and the clips drop. There's no magnet anywhere in the setup: just a nail, some wire, and a battery.

Two ideas explain where the magnet came from:

  1. Magnets surround themselves with a field. It has a north pole and a south pole, it can be mapped with lines, and like poles repel while unlike poles attract.
  2. Electricity and magnetism are the same force. A current makes a magnetic field, and a changing magnetic field makes a voltage. Those two facts run electromagnets, motors, generators, transformers, and, in the end, radio.

One of Four ForcesπŸ”—

Physics recognizes four fundamental forces: gravity, the strong and weak nuclear forces (which only act inside atoms), and electromagnetism. The attraction between electrons and the nucleus in Conductors, Insulators, and Semiconductors is electromagnetism, and so is the pull of a fridge magnet. They look like different forces, but they're two faces of one, and the second half of this article shows how they connect.

Idea One: Magnets and Their FieldsπŸ”—

The space around a magnet, where its force can be felt, is its magnetic field. The field can't be seen, but it can be mapped: iron filings sprinkled around a magnet line up into curves, and a small compass placed anywhere in the field points along them. Those curves are drawn as field lines.

A 3D bar magnet, north end red and south end blue, with field lines leaving the north pole, curving around both sides, and entering the south pole; the lines crowd together near the poles where the field is strongest.

Field lines leave the north pole and curve round to the south.

Field lines follow a few rules:

  • They leave the north pole and enter the south pole (outside the magnet), and run on through the magnet to form closed loops.
  • They never cross.
  • They crowd together where the field is strong, which is why a magnet is strongest at its poles.

Poles always come in pairs. Cut a bar magnet in half and you don't get a separate north and south: you get two smaller magnets, each with both poles.

Like Poles Repel, Unlike Poles AttractπŸ”—

Bring two magnets together and their fields interact. A north pole facing a south pole pulls the magnets together; two of the same pole push them apart.

Two pairs of bar magnets. Left: a north pole facing a south pole, with field lines running straight across the gap, pulling them together. Right: a south pole facing a south pole, with field lines bending away from each other, pushing them apart.

Opposite poles attract; matching poles repel.

That rule hides a twist. A compass needle is a small magnet, and the end marked N points north. Since unlike poles attract, the pole of the Earth near the geographic North Pole must be a magnetic south pole. The names are older than the physics.

Kinds of MagnetsπŸ”—

Magnets come in three broad kinds, defined by whether their magnetism lasts:

  • Permanent magnets

    Keep their magnetism indefinitely. Ferrite (ceramic) magnets are cheap and common in fridge magnets and loudspeakers; alnico (aluminium, nickel, cobalt) was common in older equipment; neodymium magnets are the strongest ordinary magnets made. Wikipedia's Magnet article sorts magnetic materials into "soft" ones like annealed iron, "which can be magnetized but do not tend to stay magnetized," and "hard" ones, "which do": permanent magnets are made from the hard kind, which is why one is far more likely to be steel than brass, copper, or aluminium, none of which is magnetic at all.

  • Temporary magnets

    Materials like soft iron and steel become magnetic while they sit in a field, then mostly lose it when the field is taken away. A nail stuck to a magnet can pick up a paper clip of its own.

  • Electromagnets

    A coil of wire carrying current, usually around an iron core. Their strength can be turned up, down, or off with the current. The second half of this article explains them.

How Strong Is a Field?πŸ”—

Field strength is measured in tesla (T), a large unit: everyday fields are usually given in millitesla (mT) or microtesla (Β΅T), using the prefixes from Metric Prefixes and Units.

A log scale of magnetic field strength from 10 microtesla to 10 tesla: Earth's field at 31 to 58 microtesla, a fridge magnet at 1 to 10 millitesla, a small neodymium magnet near 0.1 tesla, a loudspeaker's magnet gap at 1 to 2.4 tesla, and an MRI scanner at 1.5 to 7 tesla.

From the Earth's gentle field to a hospital scanner, a range of about a hundred thousand times.

Idea Two: Electricity and Magnetism Are One ForceπŸ”—

The connection between electricity and magnetism was found by accident. In 1820, the Danish physicist Hans Christian Ørsted noticed that a compass needle swung when he switched on a current in a nearby wire. A current makes a magnetic field.

A Current Makes a FieldπŸ”—

The field around a straight wire forms rings centred on the wire. Its direction follows the right-hand rule: point your right thumb along the conventional current (Current), and your fingers curl the way the field circles.

Left: a copper wire carrying current upward, surrounded by rings of magnetic field, with the right-hand rule: thumb along the current, fingers curling with the field. Right: the same wire wound into a coil, whose rings add into a field like a bar magnet's, with a north and a south end.

One wire makes rings; a coil adds them into a bar magnet's field.

One wire's field is weak, but winding the wire into a coil adds every turn's rings together, and the result is a field shaped exactly like a bar magnet's, with a north end and a south end. Put an iron core inside and the iron's own magnetism lines up with the coil's field and multiplies it many times over. That's an electromagnet, and it's the nail puzzle solved.

A steel nail wrapped in copper wire, wired to a battery through a switch. With the switch closed, current flows, the nail becomes a magnet, and paper clips cling to its tip. With the switch open, no current flows and the clips fall away.

The coil makes the field; the steel nail concentrates it; the switch turns it on and off.

The magnet was the current all along. The coil of wire made a field the moment current flowed, the steel nail concentrated it, and opening the switch stopped the current and the field together. More turns, more current, or a better iron core all make an electromagnet stronger.

Electromagnets are everywhere a magnet needs to be switched:

  • Relays use a small current in a coil to pull a switch closed, so a small signal can control a large load.
  • Motors use electromagnets pushing against permanent magnets (or each other) to turn a shaft.
  • Loudspeakers push a coil back and forth against a permanent magnet in time with the audio signal.

A Changing Field Makes a VoltageπŸ”—

In 1831, Michael Faraday found the reverse: a magnetic field can push a current, but only when it's changing. Move a magnet into a coil and a meter connected to the coil swings. Hold the magnet still and the meter reads zero. Pull it out and the meter swings the other way. This is electromagnetic induction.

Three scenes of a magnet and a coil connected to a meter. Moving the magnet into the coil swings the needle one way. Holding the magnet still gives no reading. Pulling it out swings the needle the other way.

Motion, not presence: only a changing field induces a voltage.

Induction is what makes a generator work. AC vs DC showed a loop turning between magnet poles: the field through the loop keeps changing as it turns, so a voltage keeps being induced, first one way and then the other. That's alternating current.

TransformersπŸ”—

Induction also lets two coils share energy without touching. Wind two coils on one iron core and feed AC into the first (the primary). Its constantly changing field circulates through the core and induces a voltage in the second coil (the secondary).

A transformer: a square iron core with a primary coil of many turns on the left, fed 120 volts AC, and a secondary coil of one tenth as many turns on the right, delivering 12 volts AC. The changing field circulates through the core.

The voltage ratio follows the turns ratio.

Every turn of each coil sees the same changing field, so the voltages are in the same ratio as the number of turns:

\[ \frac{V_{\text{secondary}}}{V_{\text{primary}}} = \frac{N_{\text{secondary}}}{N_{\text{primary}}} \]

A transformer with ten times as many turns on its primary steps 120 V down to 12 V. Turn it around and it steps voltage up instead, which is how the grid reaches the high voltages that Ohm's Law and Power showed are needed for long lines. A steady DC current makes a steady field, which induces nothing, which is why transformers only work on AC.

Schematic: a 120 volt AC source connected to a transformer's primary winding, drawn as a coil, with two parallel lines marking an iron core and a smaller secondary coil on the other side, labelled 10 to 1, feeding a 12 volt load resistor.

A transformer in a schematic: two coils, with two straight lines between them for the iron core.

Current and PowerπŸ”—

A transformer can't create energy, so stepping the voltage down must step the current up. In an ideal transformer the power in equals the power out, and the currents go the opposite way to the voltages (Transformer on Wikipedia):

\[ \frac{V_{\text{primary}}}{V_{\text{secondary}}} = \frac{I_{\text{secondary}}}{I_{\text{primary}}} = \frac{N_{\text{primary}}}{N_{\text{secondary}}} \]

Two panels for an ideal 10 to 1 transformer. The primary has 120 volts and 0.5 amps, 60 watts, and looks like 240 ohms. The secondary has 12 volts and 5 amps, also 60 watts, into a 2.4 ohm load. The voltage steps down ten times, the current up ten times, and the impedance a hundred times, the square of the turns ratio.

Same 60 W on both sides; voltage and current trade places.

The 10 : 1 transformer above delivers 12 V at 5 A to its load while drawing only 0.5 A at 120 V from the wall. That's why a transformer's size is set by the power it handles, and why its rating is given in volt-amperes (VA), the product of its voltage and current.

The same trade changes how a load looks from the other side. The 2.4 Ξ© load on the secondary draws 0.5 A at 120 V from the primary, so the wall sees 240 Ξ©: a hundred times more, the turns ratio squared. Wikipedia states the rule: the load "referred to the primary circuit is equal to the turns ratio squared times the secondary circuit load impedance." Transformers use this to make a load look like the resistance a source wants to drive, which is how audio amplifiers drive loudspeakers and how radio antennas are matched to their cables.

Where the Losses GoπŸ”—

Real transformers lose a little energy on the way through, as heat, in four ways:

Four panels of transformer losses. Copper loss: the windings' own resistance heats with the current squared. Eddy currents: loops of current induced in the iron core, large in a solid core and cut by a laminated stack of thin sheets. Hysteresis: energy spent re-magnetising the core every half-cycle. Leakage flux: field that misses the other winding. Distribution transformers still run 98 to 99 percent efficient.

Every loss ends as heat, which is why a working transformer is warm.
  • Copper loss: the windings are wire, and wire has resistance, so current through them makes heat that grows with the current squared.
  • Eddy currents: the iron core is a conductor too, and the changing field induces loops of current inside it. Building the core from thin, insulated sheets, called laminations, breaks those loops up; Wikipedia notes that "thinner laminations reduce losses, but are more laborious and expensive to construct."
  • Hysteresis: the core's magnetism reverses every half-cycle, and "each time the magnetic field is reversed, a small amount of energy is lost."
  • Leakage flux: some of the field misses the second winding and does no useful work.

None of these is large in a well-made transformer: Wikipedia puts typical distribution transformers at 98 to 99% efficient.

Kinds of TransformerπŸ”—

The same two-winding idea comes in a few arrangements worth recognizing:

Three transformer schematics. An isolation transformer with two separate windings in a 1 to 1 ratio. A transformer whose secondary has a centre tap, a connection at its midpoint. And an autotransformer: a single winding, with the input across all of it and the output taken from a tap partway along, so input and output share a connection.

Two separate windings isolate; one shared winding doesn't.
  • Isolation transformer: a 1 : 1 transformer used for safety. The output has the same voltage as the input, but "no conductive path is present between source and load" (Isolation transformer), so touching one side of the output while standing on the ground doesn't complete a path back through the mains.
  • Centre-tapped secondary: a connection halfway along the secondary gives two equal voltages either side of the tap, which some full-wave rectifiers use (Diodes and LEDs).
  • Multiple windings: one primary can feed several secondaries at different voltages, each isolated from the others.
  • Autotransformer: "an electrical transformer with only one winding" (Autotransformer), with the output taken from a tap. It's smaller and cheaper, but it gives no isolation at all.
  • Variac: a variable autotransformer whose sliding contact runs along the winding, giving a smoothly adjustable AC voltage. It's a repair-shop tool for testing equipment at different voltages, and, being an autotransformer, it doesn't isolate either.
  • Toroidal: wound on a ring-shaped core, which keeps nearly all its field inside the ring, so it leaks less field and less interference into the circuits around it (Inductor on Wikipedia).

An Autotransformer or Variac Is Not Isolated

Because input and output share one winding, an autotransformer's output is connected to the mains. Wikipedia warns that a failure in one "can result in full input voltage applied to the output." Never treat a variac's output as safer than the wall outlet it plugs into.

From Fields to RadioπŸ”—

A current makes a magnetic field; a changing magnetic field makes a voltage. In 1865, James Clerk Maxwell worked out that changing electric and magnetic fields can keep generating each other and travel through space on their own, at the speed of light. In 1887, Heinrich Hertz, the man the unit of frequency is named after, made and detected those waves in his laboratory. They're radio waves: electromagnetism set loose from the wire. Exploring Radio picks up the story from there.

Safety: Strong MagnetsπŸ”—

Small, powerful magnets, like the neodymium magnets used in craft projects and magnet sets, are a real hazard around children.

Swallowed Magnets Are a Medical Emergency

Health Canada warns that swallowing small, powerful magnets can cause severe injury or death, with children under 10 most at risk. Two or more swallowed magnets can attract each other through the walls of the intestines and tear them. Keep loose small magnets away from children, and get medical help immediately if one may have been swallowed.

Larger neodymium magnets carry their own risks.

Pinches, Shards, and Electronics

Strong magnets snap together hard enough to pinch skin painfully and can shatter into sharp shards when they collide. Magnet suppliers also warn to keep them away from pacemakers and other implanted medical devices, and from the magnetic stripes on cards.

PracticeπŸ”—

1. Which Way?

A magnet's north pole is brought near another magnet's north pole. What happens?

Solution

They repel. Like poles push apart; only unlike poles (north and south) attract.

2. Cutting a Magnet

A bar magnet is cut in half across its middle. How many poles does each half have?

Solution

Two. Each half is a complete magnet with its own north and south pole; poles always come in pairs.

3. A Stronger Electromagnet

Name three ways to make the nail electromagnet stronger.

Solution

Use more turns of wire, more current (within what the wire and battery can safely handle), and a better iron core. Each one increases the field.

4. Still Magnet

A strong magnet sits motionless inside a coil connected to a meter. What does the meter read, and why?

Solution

Zero. Induction needs a changing field. A stationary magnet makes a steady field, which induces no voltage.

5. Turns Ratio

A transformer has 600 turns on its primary and 30 on its secondary. With 120 V AC on the primary, what's the secondary voltage?

Solution

\( 120 \times 30 / 600 = 6\ \text{V} \) AC. The ratio is 20 : 1, so the voltage steps down twenty times.

6. Why Not DC?

Why won't a transformer step down the 12 V DC from a car battery?

Solution

Steady DC makes a steady magnetic field in the core, and a steady field induces no voltage in the secondary. A transformer needs a changing current, which is why it works on AC.

7. Secondary Current

A transformer steps 120 V down to 12 V and draws 0.5 A from the wall. Ignoring losses, how much current can its secondary deliver?

Solution

Power in equals power out: 120 V Γ— 0.5 A = 60 W, so the secondary delivers 60 W Γ· 12 V = 5 A. The voltage went down ten times, so the current went up ten times.

8. Step Up, Current Down

A transformer with a 1 : 5 turns ratio steps a voltage up and delivers 50 mA to its load. Ignoring losses, what current does its primary draw?

Solution

The voltage goes up five times, so the current on the primary side is five times the secondary current: 5 Γ— 50 mA = 250 mA.

9. Is It Isolated?

A variac and a 1 : 1 isolation transformer both deliver 120 V AC. Which one isolates its output from the mains, and why?

Solution

The isolation transformer. Its two windings share only the magnetic field, with no conductive path between them. A variac is an autotransformer: one winding, with input and output connected through it.

Quick RecapπŸ”—

  • Fields and poles

    Field lines leave north and enter south, never cross, and crowd where the field is strong.

  • Attract and repel

    Unlike poles attract; like poles repel. Poles always come in pairs.

  • Kinds of magnets

    Permanent (ferrite, alnico, neodymium), temporary (soft iron), and electromagnets.

  • Current makes a field

    Ørsted, 1820. A coil with an iron core is an electromagnet.

  • Changing field makes a voltage

    Faraday, 1831. Induction runs generators and transformers.

  • Transformers

    Voltage ratio = turns ratio; current ratio is the inverse; power in = power out. AC only.

What's NextπŸ”—

With electricity and magnetism joined, Series and Parallel Circuits returns to building real circuits from several components.

Further ReadingπŸ”—

Reference

Deep Dives

Related Articles

  • AC vs DC β€” the generator that induction makes possible
  • Ohm's Law and Power β€” why transformers step the grid up to high voltage
  • Current β€” the conventional current direction the right-hand rule uses