The force of magnetism is the physical push or pull exerted by a magnetic field on a ferromagnetic material, moving charge, or another magnetic field, measured in Newtons (N) or pounds-force (lbf). When you are designing a custom maglock, sizing a solenoid valve for a pneumatic circuit, or picking a stepper motor for a CNC router, this force is the exact number that dictates whether your mechanism actuates reliably or stalls out under load.
In a real circuit or mechanical installation, the force of magnetism changes the physical mechanical work your electronics can perform. It determines if a 5V relay has enough contact pressure to carry 10A without arcing, or if a 12V solenoid can physically pull a 2kg steel deadbolt against a spring. What people most commonly confuse it with is magnetic flux density (measured in Tesla or Gauss)—assuming a material with a higher Tesla rating will automatically yield a stronger physical pull, which ignores the critical role of surface area.
The Math: A Worked Numeric Example of Magnetic Pull
To size an electromagnet, solenoid, or permanent magnet for a flat-face pull against a steel plate, we use the Maxwell pulling force equation. This formula bridges the gap between the electrical/magnetic domain and the mechanical domain.
Where: F = Force (Newtons), B = Flux density at the gap (Tesla), A = Pole face area (m²), μ₀ = Vacuum permeability (≈ 1.2566 × 10⁻⁶ T·m/A)
Let us calculate the theoretical holding force of a DIY DC solenoid you are winding for a custom cabinet lock.
- Flux Density (B): Your mild steel plunger saturates around 1.2 Tesla at the contact face.
- Plunger Diameter: 10 mm (0.01 m). The area (A = π × r²) is π × (0.005)² = 7.854 × 10⁻⁵ m².
- Permeability (μ₀): 1.2566 × 10⁻⁶ T·m/A (per the NIST CODATA vacuum permeability value).
Plugging in the numbers:
F = (1.2² × 7.854 × 10⁻⁵) / (2 × 1.2566 × 10⁻⁶)
F = (1.44 × 7.854 × 10⁻⁵) / (2.5132 × 10⁻⁶)
F = 0.00011309 / 0.0000025132
F ≈ 45 Newtons
Where You Meet the Force of Magnetism in Practice
You will encounter this physical force in several common maker and electrical scenarios:
- Solenoid Actuators: Used in 3D printer filament cutters, automatic pet feeders, and pneumatic valves. The force dictates the maximum spring return tension you can use.
- Electromechanical Relays: The armature must generate enough magnetic force to overcome the spring tension and close the contacts with sufficient pressure to maintain a low-resistance electrical path.
- Magnetic Latches (Maglocks): Used in CNC enclosure doors and automated greenhouse vents. These rely on a large surface area (A) rather than extreme flux density (B) to achieve holding forces exceeding 200 kg.
- Stepper and BLDC Motors: The rotational torque is fundamentally derived from the tangential force of magnetism acting on the rotor's radius. If the load exceeds this force, the motor stalls and skips steps.
Common Confusions: Flux Density vs. Actual Pulling Force
The most frequent mistake DIYers make when ordering magnets from suppliers is chasing the highest grade (like N52 neodymium) while ignoring the physical dimensions.
Think of magnetic flux density (Tesla) like the vacuum pressure inside a suction cup, and the pole area as the physical size of the cup. A tiny 3mm N52 cube has an incredibly high vacuum pressure (up to 1.48 T), but because the suction cup is so small, the total pulling force is barely enough to hold a piece of paper. Conversely, a massive N35 ceramic ferrite magnet has a much lower flux density (around 0.4 T), but its massive surface area generates hundreds of Newtons of total pull.
When sizing components, always look at the manufacturer's pull-force curves (like those provided by K&J Magnetics Theory and Calculators) rather than just the material grade. Force scales linearly with area, but exponentially with the air gap distance (following an inverse-cube law for dipole fields).
Decision Tree: Picking the Right Actuator for Your Build
Use this matrix to select the correct magnetic actuator for your project. Follow the conditions down to the recommended part.
| Application Requirement | If True... | If False... |
|---|---|---|
| Does the mechanism need to hold indefinitely without consuming continuous electrical power? | Use a Permanent Magnet (Neodymium or SmCo) with a mechanical release lever. | Proceed to next question. |
| Must the lock/actuator automatically release (fail-safe) if the power drops? | Use an Electromagnet / Maglock (continuous duty coil). | Proceed to next question. |
| Do you need a linear mechanical stroke (push/pull) greater than 2mm against a spring? | Use an Intermittent Duty Solenoid. | Use a Relay or Micro-solenoid. |
Frequently Asked Questions
Does painting or powder-coating a magnet reduce its pulling force?
Yes, but only because it introduces an air gap. The force of magnetism drops off drastically with distance. A standard 0.1mm powder coat will reduce the surface pull force of a neodymium magnet by roughly 10% to 15%. If maximum force is required, use a bare, nickel-plated magnet and ensure the mating steel surface is also bare and perfectly flat.
Why did my MOSFET explode when I turned off my DIY electromagnet?
You experienced inductive kickback. When you cut power to a coil, the collapsing magnetic field induces a massive reverse voltage spike (often hundreds of volts) that destroys silicon components. You must always wire a flyback diode (like a 1N4007) in reverse parallel across the solenoid or electromagnet coil to safely dissipate this energy.
Can I increase the force of an electromagnet by just turning up the voltage?
Only up to the point of core saturation. Increasing voltage increases current, which increases the magnetic field (H). However, once the steel core reaches its saturation flux density (usually between 1.5T and 2.0T for mild steel), no amount of extra current will increase the pulling force. Beyond saturation, you are just generating waste heat and risking a coil fire. If you need more force after saturation, you must increase the physical cross-sectional area of the core.
