What Is an Electromagnet and How Does It Work? Core Theory & Sizing

An electromagnet is a temporary magnet created by passing an electric current through a coil of wire, usually wrapped around a ferromagnetic core, generating a magnetic field that disappears when the current stops. In a real circuit, adding an electromagnet introduces significant inductance, which resists changes in current, causes phase shifts in AC systems, and generates destructive high-voltage spikes when switched off in DC systems. Beginners frequently confuse general electromagnets with solenoids; while a solenoid is a specific type of electromagnet engineered to produce linear mechanical motion (like a plunger), a standard electromagnet is primarily designed to generate a static magnetic holding force or transfer magnetic flux.

The Physics of the Coil: Ampere-Turns and Reluctance

To understand how an electromagnet works, you have to look past the physical wire and focus on the magnetic circuit. The strength of an electromagnet is not determined by voltage alone, but by its Magnetomotive Force (MMF), measured in Ampere-turns (AT). The formula is straightforward:

MMF = N × I

Where N is the number of wire turns and I is the current in amperes. You can achieve 1,000 AT by pushing 10 amps through 100 turns, or by pushing 0.1 amps through 10,000 turns. The physical limits of your wire gauge and power supply dictate which route you take.

However, MMF is just the 'pressure' pushing the magnetic field. The actual magnetic flux (measured in Webers) depends on the reluctance of the core material. Think of magnetomotive force (MMF) as water pressure, the magnetic flux as the water flow rate, and the core's reluctance as a narrow section of pipe resisting that flow. Air has incredibly high reluctance. If your coil is just wrapped around a plastic tube (an air-core electromagnet), most of your MMF is wasted. By inserting a ferromagnetic core—like mild steel, silicon steel, or iron—you drop the reluctance by a factor of 1,000 to 5,000, concentrating the flux lines into a powerful, usable magnetic field.

According to Georgia State University's HyperPhysics, the permeability of the core material is the critical multiplier in electromagnet design, but it comes with a catch: magnetic saturation. Once all the magnetic domains in the steel core are aligned, adding more current yields almost zero additional holding force, and all that extra electrical energy simply turns into waste heat.

Worked Example: Sizing a 12V DC Bench Electromagnet

Let’s move from theory to the workbench. Suppose you need to wind a 12V DC holding electromagnet to act as a custom magnetic lock for a cabinet door. You want a continuous duty cycle (it stays on indefinitely) without melting the insulation off the wire.

Step 1: Calculate Required Resistance
Using Ohm’s Law (R = V / I), we need a total coil resistance of 12V / 0.5A = 24 Ω.

Step 2: Calculate Wire Length
Since 26 AWG wire has 40.81 Ω per 1,000 ft, the length required for 24 Ω is:
(24 Ω / 40.81 Ω) × 1,000 ft = 588 feet of wire.

Step 3: Calculate Number of Turns
The average length of one turn around the 1.5-inch form is 4.71 inches, or 0.3925 feet.
588 ft / 0.3925 ft per turn = 1,498 turns.

Step 4: Calculate Magnetomotive Force (MMF)
MMF = 1,498 turns × 0.5A = 749 Ampere-turns.

This 749 AT coil will generate a surprisingly strong holding force on the mild steel rod—easily enough to hold a 15 lb steel plate flush against the pole face. As noted in the All About Circuits DC textbook, the tightness of the winding and the physical contact area between the core and the target metal will ultimately dictate the real-world pull force, but the electrical sizing guarantees the coil won't burn up on your bench.

Where You Meet Electromagnets in Practice (And What Confuses Makers)

You interact with electromagnets constantly in electrical installations and electronics projects, though they are usually hidden inside other components.

• Relays and Contactors: The 'coil' listed on a relay datasheet is just an electromagnet. When energized, it pulls a steel armature that closes the high-current mechanical contacts.
• Transformers: A transformer is essentially an AC electromagnet. The primary winding creates a constantly collapsing and expanding magnetic field in the laminated silicon-steel core, which induces a voltage in the secondary winding.
• Maglocks (Electromagnetic Locks): Used in commercial access control. These are pure, massive electromagnets designed for maximum holding force (often 1,200 lbs) rather than mechanical movement.

The Solenoid Confusion: Makers often use the terms interchangeably, but a solenoid is designed to move a plunger through the center of the coil to do mechanical work (like a starter motor solenoid or a sprinkler valve). An electromagnet is designed to hold a surface against its pole face. Solenoids usually have high inrush currents and require duty-cycle limits to prevent overheating, whereas holding electromagnets are often designed for continuous 100% duty cycles.

The Inductive Kickback Hazard: Because an electromagnet is a massive inductor, it stores energy in its magnetic field. When you abruptly cut power to a DC electromagnet using a transistor or a microcontroller GPIO pin, the collapsing magnetic field induces a massive reverse voltage spike (often hundreds of volts). If you wire a 12V relay coil directly to an ESP32 or Arduino without a flyback diode (like a 1N4007 wired in reverse across the coil terminals), that voltage spike will travel backward and instantly brick your microcontroller's silicon. Always provide a path for the inductive energy to dissipate.