Understanding the Basics of Magnetism in Electrical Circuits

Magnetism is a fundamental physical force produced by the motion of electric charges, resulting in attractive and repulsive interactions between objects. In a real circuit or installation, magnetism changes how energy is stored, transferred, and dissipated—dictating the physical size of transformer cores, the torque curve of a BLDC motor, and the destructive voltage spikes that fry MOSFETs when you switch off an inductive load. Beginners commonly confuse magnetic field strength (H, measured in Amperes per meter) with magnetic flux density (B, measured in Teslas), assuming they are interchangeable when they are actually linked by the core material's permeability.

Magnetic Core Materials and Saturation Limits

To design or troubleshoot inductive components, you must understand how different materials respond to a magnetic field. The two most critical specifications on any magnetics datasheet are relative permeability ($\mu_r$), which dictates how easily the material supports a magnetic field, and saturation flux density ($B_{sat}$), the absolute limit of magnetic flux the material can hold.

How to read this table: Notice the tradeoff between permeability and saturation. Ferrite has decent permeability but saturates very early (~0.4 T), making it useless for 60Hz mains transformers but perfect for high-frequency switch-mode supplies where flux swings are kept intentionally small to minimize core losses. Silicon steel handles massive flux densities (~2.0 T) but suffers from high eddy current losses at high frequencies, which is why it is laminated into thin sheets for 50/60Hz applications.

Worked Example: Sizing a Solenoid and Hitting Saturation

Let's calculate the magnetic flux density ($B$) inside a custom DC solenoid to see how core selection and saturation work in practice. The formula for the flux density inside a long solenoid is:

$B = \mu_0 \cdot \mu_r \cdot n \cdot I$

• $\mu_0$ (Vacuum permeability): Since the 2019 SI redefinition of the Ampere, $\mu_0$ is no longer exactly $4\pi \times 10^{-7}$, but rather an experimentally determined value of approximately $1.2566 \times 10^{-6}$ T·m/A. For bench-level engineering, $1.257 \times 10^{-6}$ is perfectly adequate.
• $\mu_r$ (Relative permeability): 1 for air, ~4000 for GOSS.
• $n$ (Turn density): Total turns ($N$) divided by coil length ($l$).
• $I$ (Current): Amperes.

The Scenario: You wind 200 turns of 22 AWG magnet wire over a 0.1-meter long bobbin ($n = 2000$ turns/m). You drive it with 0.2A of DC current.

Calculation 1: Air Core ($\mu_r = 1$)
$B = (1.2566 \times 10^{-6}) \cdot 1 \cdot 2000 \cdot 0.2 = 0.0005$ Teslas (0.5 mT).
Result: Extremely weak. Barely enough to pick up a paperclip.

Calculation 2: GOSS Core ($\mu_r = 4000$)
$B = (1.2566 \times 10^{-6}) \cdot 4000 \cdot 2000 \cdot 0.2 = 2.01$ Teslas.
Result: The math says 2.01 T, but looking at our table above, GOSS saturates at roughly 2.0 T.

Where You Meet Magnetism in Practice

Abstract theory only matters when it burns a component or fails an EMC test. Here is where the basics of magnetism dictate your physical design choices on the bench or in the panel.

1. Inductive Kickback and Flyback Diodes

When current flows through an inductor or relay coil, energy is stored in the magnetic field ($E = \frac{1}{2}LI^2$). If you open a mechanical switch or turn off a MOSFET to break the circuit, the magnetic field collapses rapidly. Faraday's Law of Induction dictates that this collapsing field will induce a voltage spike ($V = -L \frac{di}{dt}$) of whatever magnitude is necessary to keep the current flowing. Without a flyback diode to provide a recirculation path, a 12V relay coil can generate a 200V+ spike that will instantly punch through the gate oxide of your driving logic IC.

2. EMI and PCB Trace Routing

Alternating magnetic fields induce unwanted voltages in adjacent conductors (crosstalk). On a PCB, routing a high-$di/dt$ trace (like the switch node of a buck converter) parallel to a sensitive analog feedback trace will magnetically couple noise into your control loop. The fix is physical geometry: cross sensitive traces at 90-degree angles to minimize the shared magnetic loop area, and utilize solid ground planes to provide a low-impedance return path that cancels out the magnetic field of the forward trace.

3. Transformer Volt-Second Product

When designing or selecting a transformer for a forward or flyback converter, you must respect the volt-second product. If you apply a DC voltage to a transformer primary for too long without allowing the core to reset, the flux walks up the B-H curve until it hits $B_{sat}$. Once saturated, the primary winding effectively becomes a dead short across your DC bus, resulting in catastrophic failure of the switching transistors. This is why current-mode control is heavily favored in modern SMPS design—it inherently prevents flux imbalance by monitoring the primary current cycle-by-cycle.

Common Magnetism Misconceptions