Magnetism and electromagnetism
Every current creates a magnetic field, and every magnetic field can exert a force on a current. From this back-and-forth come the motor, the relay, the speaker and — in the next topic — the transformer and the generator.
01The magnetic field
A magnet has two poles, north and south. Like poles repel, unlike poles attract. Between them there is a field represented by closed lines of force: they leave the north pole, run through the exterior, enter at the south pole and close inside the magnet.
Electric charges can be separated: there are bodies with positive charge and others with negative. Magnetic poles cannot. If you break a magnet in half you do not get a loose north pole and a loose south pole: you get two complete magnets, each with its two poles. That is why magnetic field lines are always closed, whereas electric ones begin and end on charges.
The quantities
| Quantity | Symbol | Unit | What it represents |
|---|---|---|---|
| Magnetic flux | Φ | weber (Wb) | Total number of lines passing through a surface. |
| Induction, or flux density | B | tesla (T) | Flux per unit area: how concentrated the field is. 1 T = 1 Wb/m². |
| Field strength | H | A/m | The magnetizing “effort” applied by the current, independent of the material. |
| Permeability | µ | H/m | How readily the material allows the field to be established. µ = µ0·µr. |
| Magnetomotive force | ℱ | A·turn | The “cause” of the field: ℱ = N·I. |
| Reluctance | ℛ | A·t/Wb | Opposition of the magnetic circuit to the establishment of flux. |
As a reference for real magnitudes: Earth's magnetic field is about 50 µT; a refrigerator magnet, 5 mT; the air gap of a motor, 1 T; a neodymium magnet attached to iron, 1.4 T; a hospital MRI scanner, 3 T.
02The field created by a current
Oersted discovered it by accident in 1820: a compass needle was deflected when current passed through a nearby wire. That finding united two branches of physics thought to be separate and founded everything that follows.
Inserting a soft-iron core into the solenoid, µ goes from µ0 to µ0·µr with µr of several thousand. The field is multiplied by that factor without changing anything else. That turns the coil into a powerful electromagnet and, unlike a permanent magnet, it can be switched on and off. From this come the relay, the contactor, the solenoid valve and the scrapyard crane.
03Magnetic materials
| Type | µr | Behavior | Examples |
|---|---|---|---|
| Diamagnetic | slightly < 1 | Slightly oppose the field; they are repelled. | Copper, silver, water, bismuth |
| Paramagnetic | slightly > 1 | Become magnetized very weakly. | Aluminum, platinum, oxygen |
| Ferromagnetic | 100 to 100,000 | Become strongly magnetized and retain part of the magnetism. | Iron, nickel, cobalt, ferrites |
Only ferromagnetics are technically useful. Their behavior is explained by magnetic domains: microscopic regions that are already magnetized and that, in a demagnetized material, point in random directions and cancel out. When an external field is applied, the domains align and the material becomes a magnet.
When all the domains are already aligned, increasing the current no longer increases the field: the core is saturated. From then on the coil behaves as if it had no core, the inductance collapses and the current shoots up. This is why a transformer fed with excessive voltage — or with direct current — overheats and burns out. In design you choose to always work below saturation: about 1.2 to 1.5 T in silicon-steel laminations, 0.3 to 0.4 T in ferrite.
04Magnetic circuits
A magnetic circuit is a closed path through which flux circulates: the core of a transformer, that of a relay, the stator of a motor. It is analyzed with a very convenient analogy: it behaves just like an electric circuit.
| Electric circuit | Magnetic circuit | Relationship |
|---|---|---|
| Electromotive force E [V] | Magnetomotive force ℱ = N·I [A·t] | The cause |
| Current I [A] | Flux Φ [Wb] | The effect |
| Resistance R = ρ·L/A | Reluctance ℛ = L/(µ·A) | The opposition |
| Ohm's law: I = E/R | Hopkinson's law: Φ = ℱ/ℛ | The law |
| Resistances in series add | Reluctances in series add | Combination |
A toroidal iron core (µr = 2000) with a mean length of 20 cm and a cross-section of 4 cm², with an air gap (a slot of air) of 1 mm. A winding of 500 turns carrying 2 A.
Reluctance of the iron:
ℛFe = 0.199 / (4π×10−7 × 2000 × 0.0004) = 198,000 A·t/Wb
Reluctance of the air gap (air, µr = 1):
ℛair = 0.001 / (4π×10−7 × 1 × 0.0004) = 1,990,000 A·t/Wb
The air gap is 0.5 % of the length of the circuit and yet contributes ten times more reluctance than all the iron. Total: ℛ = 2,188,000 A·t/Wb, and
Φ = (500 × 2) / 2,188,000 = 0.457 mWb → B = Φ/A = 1.14 T
Without the air gap the flux would be 5 mWb and B would reach 12.6 T: impossible, the core saturates long before. Conclusion: in a magnetic circuit with an air gap, the air gap dominates the calculation. That is why transformer cores are built with interleaved E-I laminations, so that no air gap is left.
05Force on a current-carrying conductor
The reciprocal of Oersted's effect: a conductor carrying current, placed inside a magnetic field, experiences a force.
With the left hand: the index finger points in the direction of the field (from N to S), the middle finger in the direction of the current, and the thumb indicates the force. It is the rule that explains the direction of rotation of every DC motor.
Be careful not to mix it up with the right-hand rule, which is used for the field a current creates and for the voltage induced in a generator.
A conductor 8 cm long inside a 0.8 T field with 5 A perpendicular to it:
F = 0.8 × 5 × 0.08 = 0.32 N
Not much. But a winding with 200 active conductors gives 64 N, and multiplied by the rotor radius you get the torque. That is why motors have many turns and not a single loop.
06Direct applications
An electromagnet attracts an armature that closes or opens mechanical contacts. It lets a low-voltage, low-current circuit (the output of a microcontroller, via a transistor) drive a 220 V load of several amperes, with total galvanic isolation between the two.
Specifications to check: coil voltage (5, 12, 24 V), coil current, and contact rating (for example “10 A / 250 V~”). And always the flyback diode, as seen in the transistor as a switch — which the transistors article shows working with an LED.
A moving coil attached to the cone, inside the field of a permanent magnet. The audio current produces a force F = B·I·L that pushes the cone back and forth following the signal.
It is the same mechanism as the moving-coil galvanometer, only without restoring springs and optimized to move quickly. It also works in reverse: pushing the cone generates voltage, which is exactly how a dynamic microphone works.
A winding (rotor) inside the field of a magnet or of another winding (stator). The Laplace force makes it turn; the commutator and the brushes reverse the current every half turn so that the torque does not change direction.
A solenoid that attracts a metal plunger and opens or closes the passage of a fluid. It is the most common actuator in pneumatics and hydraulics, a subject of Industrial Electronics II in Year 7.
07In the lab
A compass beneath a straight conductor connected to a battery through a current-limiting resistor. When the circuit is closed the needle deflects; when the polarity is reversed, it deflects to the other side. Verify the direction with the right-hand rule. Move the compass away and check that the deflection decreases (B falls off as 1/r).
Wind 200 turns of 0.5 mm enameled wire onto a large nail. Power it with 6 V through a resistor (measure the current) and count how many paper clips it lifts.
- Double the current and count again.
- Double the turns keeping the original current and count again.
- Remove the nail and repeat with an air core.
The three results verify that what matters are the ampere-turns and that the ferromagnetic core multiplies the effect. Watch out for the winding heating up: do not leave it connected for more than a few seconds.
Iron filings on a sheet of paper or acetate, with a magnet underneath. Tap the paper gently: the filings orient themselves and trace the lines. Repeat with two magnets facing each other with like poles and with opposite poles. Then replace the magnet with a powered solenoid and compare the shape of the field: it is practically the same.
A piece of rigid wire hanging between the poles of a horseshoe magnet, connected to a current-limited power supply. When the circuit is closed the wire jumps outward or inward depending on the polarity. Verify with the left-hand rule. It is the direct demonstration of the motor principle.
08Common mistakes
| Confusion | Clarification |
|---|---|
| Mixing up B and H | H is what the current applies (N·I/L, does not depend on the material); B is the resulting field (B = µ·H, does depend on the material). |
| Mixing up the right hand and the left | Right: field a current creates, and induced voltage. Left: force on a current-carrying conductor (motor). |
| Believing a magnetic pole can be isolated | Breaking a magnet gives two complete magnets. Magnetic monopoles do not exist. |
| The electromagnet lifts nothing | Too few ampere-turns, or a core of non-ferromagnetic material (aluminum and bronze do not work). |
| The electromagnet heats up and does not improve when the voltage is raised | Saturated core: all the domains are already aligned and only the Joule loss increases. |
| The magnetic circuit calculation gives an absurd flux | The air gap was forgotten; it usually dominates the total reluctance even if it is only a millimeter. |
| The core stays magnetized after switching off | Remanent magnetism. It is normal in iron; relay cores use soft iron and sometimes an anti-remanence stop precisely for that reason. |
09Self-assessment
Why are magnetic field lines closed and electric ones not?
Because magnetic monopoles do not exist: there is no “loose north pole” where a line could begin. Electric lines, on the other hand, begin on positive charges and end on negative ones, which can indeed be separated.
A solenoid of 300 turns and 15 cm length carrying 2 A with an air core. What is B?
B = µ₀·N·I/L = 4π×10−7 × 300 × 2 / 0.15 = 5.0 mT. With an iron core of µr = 2000 it would rise to about 10 T in theory, but the core would saturate long before (at around 1.5 T).
What are ampere-turns and why do they matter?
They are the product N·I, the magnetomotive force. What determines the field is not the current alone nor the turns alone but their product: 1000 turns with 0.1 A produce the same as 100 turns with 1 A. The combination is chosen according to the available source and the acceptable dissipation.
What does it mean for a core to be saturated?
That all its magnetic domains are already aligned and increasing the current no longer increases B. The inductance collapses, the current grows out of control and the winding heats up. It is what happens to a transformer if it is fed excessive voltage or direct current.
In a magnetic circuit with a 1 mm air gap, why does the air gap dominate?
Because the reluctance is ℛ = L/(µ·A), and in air µr = 1 whereas in iron it is in the thousands. Even though the air gap is 200 times shorter than the iron, its reluctance can be 10 times greater. That is why transformer laminations are interleaved without leaving gaps.
A 20 cm conductor carrying 3 A, inside a perpendicular 0.5 T field. What force does it experience?
F = B·I·L·sin 90° = 0.5 × 3 × 0.2 = 0.3 N. If the conductor were parallel to the field, the force would be zero.
What advantage does a relay offer over a transistor driving the load directly?
Galvanic isolation: there is no electrical connection between the control circuit and the power circuit. It also handles AC and DC indifferently, tolerates overloads and its closed contact has almost zero resistance. In exchange it is slow, noisy, wears out and needs more drive current.
Why are a speaker and a dynamic microphone the same device?
Because the coil-magnet mechanism works in both directions: if current is injected, a force appears and the cone moves (speaker); if the cone is moved, a voltage is induced (microphone). A small speaker really does work as a microphone, and it is a classic experiment.