How Inductors Work: Magnetic Fields, Energy Storage & LC Circuits

What Is an Inductor?

At its heart, an inductor is simply a coil of wire. When current flows through a conductor, it creates a surrounding magnetic field (per Ampere's Law). By coiling the wire, each loop's magnetic field adds together, creating a strong concentrated magnetic flux through the center of the coil.

The key property of an inductor is its opposition to changes in current — described mathematically by Faraday's Law of Electromagnetic Induction. When current tries to increase, the inductor generates a back-EMF (electromotive force) that opposes the increase. When current tries to decrease, it generates a forward EMF to maintain the current flow.

Faraday's Law & Self-Inductance

The voltage across an inductor is governed by Faraday's Law of Induction:

V = L × (dI / dt)

Where V is the induced voltage in Volts, L is the inductance in Henrys, and dI/dt is the rate of change of current in Amperes per second.

This equation tells us something critical: the faster current tries to change, the larger the opposing voltage. An inductor's self-inductance (L) depends on:

• Number of turns (N²): Inductance scales with the square of the number of turns. Doubling turns quadruples inductance.
• Core permeability (μ): Ferrite cores have high magnetic permeability (μr = 2,000–15,000×), dramatically increasing inductance versus air-core coils.
• Cross-sectional area (A): A wider core concentrates more flux, increasing inductance.
• Core path length (l): Longer magnetic paths reduce inductance — toroidal cores minimize this by having no "air gap" in the flux path.

The RL Circuit Time Constant

When a voltage source is connected to an inductor in series with a resistor (an RL circuit), current doesn't jump instantly to its maximum value — it rises exponentially according to:

I(t) = (V/R) × (1 − e^(−t/τ))    where τ = L/R

The time constant τ = L/R dictates the speed of current rise:

Fig 1: RL circuit current rise — current reaches 63.2% of final value at t=τ=L/R

Types of Inductors & Core Materials

The core material used inside an inductor drastically changes its characteristics:

Real-World Applications of Inductors

1. DC-DC Switching Converters (Buck & Boost)

Inductors are the heart of switching power regulators. In a buck (step-down) converter, the inductor averages a pulsed high voltage into a smooth lower output. In a boost (step-up) converter, the collapsing magnetic field of the inductor generates a voltage spike higher than the input — your 3.7V LiPo cell powering a 5V USB output is a perfect example.

2. LC Oscillators & Resonant Circuits

Combined with a capacitor, an inductor forms a resonant tank circuit. The resonant frequency is:

f₀ = 1 / (2π × √(L × C))

Used in radio tuners, crystal oscillators, and bandpass filters. The capacitor and inductor exchange energy back and forth — stored alternately as electric field (C) and magnetic field (L).

3. EMI Choke Filters

Power line chokes on USB chargers and mains equipment are inductors designed to block high-frequency switching noise (EMI) from entering the power grid. Since inductive reactance XL = 2πfL scales with frequency, high-frequency noise is blocked while 50/60Hz mains current passes unimpeded.

4. Arduino Project Code: Boost Converter Output Sensing

// Read boost converter output voltage via voltage divider
// R1=10kΩ, R2=3.3kΩ → divide 12V max to 3.3V ADC range
const int voltPin = A0;
const float R1 = 10000.0, R2 = 3300.0;
const float Vref = 5.0;

void setup() { Serial.begin(9600); }

void loop() {
  int raw = analogRead(voltPin);
  float vADC = (raw / 1023.0) * Vref;
  float vBoost = vADC * ((R1 + R2) / R2);
  Serial.print("Boost Output: ");
  Serial.print(vBoost, 2);
  Serial.println(" V");
  delay(500);
}

Frequently Asked Questions

Conclusion

Inductors are the unsung heroes of power electronics and RF design. From the boost converter in your phone charger to the EMI choke on a motor driver, understanding inductance, RL time constants, and core saturation will unlock your ability to design reliable, efficient circuits.