Electromagnetism

Part of Electrical Theory

The unified relationship between electricity and magnetism—how each can produce the other, and how this relationship underlies every motor, generator, and transformer.

Why This Matters

The discovery that electricity and magnetism are manifestations of the same phenomenon was one of the greatest achievements of 19th-century physics. Before 1820, magnetism and electricity were considered separate, unrelated phenomena. Within 60 years, James Clerk Maxwell had unified them into a single elegant theory.

For practical rebuilding, this unity is more than intellectual elegance. Every device that converts electrical energy to mechanical energy (motors), every device that converts mechanical energy to electrical energy (generators), and every device that changes voltage levels (transformers) operates through the electromagnetic interaction. A person who understands how a current creates a magnetic field, and how a magnetic field creates a force on a current-carrying conductor, understands the physical mechanism behind all these devices—and can build or repair them from first principles.

Electricity Creates Magnetism

Ørsted’s discovery (1820): Hans Christian Ørsted noticed that a compass needle deflects when placed near a current-carrying wire. This was the first experimental demonstration that electricity and magnetism are related.

The magnetic field around a long, straight current-carrying wire:

• Forms circles around the wire
• Decreases in strength with distance
• Direction given by the right-hand rule: wrap the right hand around the wire with thumb pointing in the current direction; the fingers curl in the direction of the magnetic field

Right-hand rule (straight wire): Point right thumb in the direction of conventional current. Fingers curl around the wire in the direction of the magnetic field circles.

Magnetic field strength (H) near a long straight wire: H = I / (2πr)

Where I is current in amps and r is distance from the wire in meters.

Magnetic flux density (B): B = μ × H

Where μ is the permeability of the surrounding medium. For air: μ₀ = 4π × 10⁻⁷ T·m/A. For iron: μ = μ_r × μ₀ where μ_r is the relative permeability (1000–10,000 for soft iron).

This enormous permeability multiplication is why iron cores make electromagnets and transformers practical—a given coil current creates 1000–10,000× more flux in an iron core than in air.

The Electromagnet

A wire wound into a coil (solenoid) concentrates and strengthens the magnetic field:

Magnetic field inside a solenoid: B = μ₀ × μ_r × N × I / L

Where:

• N = number of turns
• I = current
• L = length of the solenoid
• μ_r = relative permeability of the core material

Ampere-turns (NI): The product of turns and current determines magnetic field strength, independent of how the turns and current are distributed. 100 turns at 1A gives the same magnetomotive force as 10 turns at 10A or 1000 turns at 0.1A.

Practical electromagnet construction:

1. Choose a soft iron core (bolt, bar, U-shape, or toroid)
2. Wind insulated copper wire: more turns = stronger field at the same current
3. Thicker wire allows more current for the same coil resistance: calculate P = I²R to stay within thermal limits
4. A horseshoe or U-shaped core with both poles at one end concentrates flux for lifting applications

Saturation: Iron core permeability is not constant—at high magnetic field levels, the iron saturates: additional current produces diminishing additional flux. Working well into saturation wastes energy as heat without proportionally increasing the magnetic field. Operate transformers and motors well below their saturation point.

Magnetism Creates Force

A current-carrying conductor in an external magnetic field experiences a force. This force is the basis of all electric motors.

Lorentz force: F = I × L × B × sin θ

Where:

• F = force (newtons)
• I = current (amps)
• L = length of conductor in the field (meters)
• B = magnetic flux density (tesla)
• θ = angle between current direction and field direction

Maximum force when θ = 90° (current perpendicular to field). Zero force when θ = 0° (current parallel to field).

Direction of force: left-hand rule (for motors, conventional current): Extend left hand with fingers pointing in current direction and bend them toward the field direction (where field lines go from N to S). The thumb points in the direction of the force on the conductor.

(Alternatively: F = I × (L⃗ × B⃗), the vector cross product of current direction and field direction. But the left-hand rule is faster for practical use.)

How a Motor Works

A motor consists of current-carrying conductors in a magnetic field. The forces on those conductors create torque (rotational force).

Simple DC motor:

1. A rectangular coil of wire sits between north and south magnetic poles
2. Current through the coil creates forces: upward on one side, downward on the other
3. These forces create a torque that rotates the coil
4. As the coil reaches the horizontal position (maximum torque), a commutator reverses the current direction
5. After reversal, the forces continue in the same rotational direction
6. The coil continues rotating

The commutator: A segmented ring with sliding brush contacts that reverses the current direction each half revolution, maintaining continuous rotation in one direction. The commutator is the mechanical component that makes DC motors possible—and the wear item that requires periodic maintenance.

AC motors (induction motors): In a three-phase AC induction motor, the three-phase currents create a rotating magnetic field without any commutator. The rotating field induces currents in the rotor (which is simply an iron cylinder with conducting bars), and the forces on these induced currents cause the rotor to spin, chasing the rotating field. No brushes, no commutator—extremely reliable and the most common industrial motor type.

Magnetism Creates Electricity

The reverse process—moving a conductor in a magnetic field inducing a current—was discovered by Faraday in 1831. See Electromagnetic Induction for the detailed treatment.

The key symmetry: the same force law (F = ILB) that drives a motor also means that moving a conductor in a field creates an EMF. A generator is simply a motor run backward mechanically.

Maxwell’s Equations

James Clerk Maxwell unified the experimental laws of Coulomb, Ampère, and Faraday into four equations that describe all classical electromagnetic phenomena:

1. Gauss’s Law for electricity: Electric fields originate at charges
2. Gauss’s Law for magnetism: Magnetic field lines form closed loops (no magnetic monopoles)
3. Faraday’s Law: Changing magnetic field creates electric field
4. Ampère-Maxwell Law: Changing electric field or current creates magnetic field

The critical insight Maxwell added: a changing electric field (not just current) creates a magnetic field. This made the equations symmetric: changing E creates B, and changing B creates E. This self-sustaining oscillation propagates through space as an electromagnetic wave—light itself.

For practical circuit work: Maxwell’s equations reduce to Kirchhoff’s Laws, Faraday’s Law, and Ohm’s Law at power frequencies and in lumped circuits. The full equations become necessary only for radio frequency circuit analysis, antenna design, and very high-speed electronics.

Magnetic Materials

Ferromagnetism: Iron, nickel, cobalt, and their alloys are strongly attracted to magnets and can be magnetized themselves. Ferromagnetic materials have very high relative permeability (μ_r = 100–100,000).

Soft magnetic materials: Easily magnetized and demagnetized. Used for transformer cores, motor cores, and relay cores where the magnetization must switch rapidly with AC or with control currents. Silicon steel (iron + 3–4% silicon) is the standard transformer core material—higher resistivity than pure iron reduces eddy current losses.

Hard magnetic materials (permanent magnets): Require high field to magnetize but retain their magnetism persistently. Used in permanent magnet motors and generators, loudspeakers, and measuring instruments. High-carbon steel, hardened iron, and alnico alloys (aluminum-nickel-cobalt) are the traditional permanent magnet materials before rare-earth magnets became available.

Curie temperature: Above a material-specific critical temperature, ferromagnetic materials lose their magnetic properties. Iron loses ferromagnetism above 770°C. Permanent magnets weakened by heating above their Curie temperature will not fully recover on cooling—a practical concern for motors and generators that run hot.