Michael Faraday and Joseph Henry discovered that wrapping coils of wire around a core induced a current. But how does inductance work?

    The secret to understanding the power that electricity can exert on the world comes from a deeper understanding of electromagnetics.

    This guide will walk you through the discovery, the calculations, and the uses of inductance in modern physics and engineering.

    When conversions get tough, use this handy calculator to go from H to Wb/A and more.


    What is inductance?

    Simply put, inductance is what an electrical conductor creates when a current runs through it.

    It takes energy, in the form of voltage, and changes it into force (in this case electromotive force).

    As we understand from basic physics, force gets things done. Force is a measure of mass accelerating.

    So electromotive force created by inductance is how current moves stuff.

    How does inductance work?

    How inductance is created and how it works gets more complicated.

    Kinetic Energy

    When a magnetic field is created it stores potential energy. The whole field is basically a bubble of energy.

    When the field collapses the potential energy becomes kinetic energy which pushes in a direction.

    This isn't too different, conceptually, from a ball falling from a height to the ground.

    Opposition Creates Force

    The biggest difference comes from how magnetic fields form based on changes in a positive and negative charge.

    This creates the complication of magnetic flux and how changes in that flux induce the voltage.

    Opposition creates force. This statement helps you understand what inductance is doing.

    Consider a ball on the ground as being at zero charge. Raising the ball to a height applies a positive charge.

    Then you can easily see that releasing the ball is applying an opposite charge that goes back to zero when returned to the ground.

    Lenz's Law

    This variation on Newton's second law of motion (every action has an equal and opposite reaction) is known as Lenz's Law.

    Paraphrased it states change and/or motion in magnetic fields induce current which directly opposes change in flux and therefore exerts force.

    What are the standard units of inductance?

    Let's get into the inductance units, and hopefully, this will help clear up any lingering confusion.

    The Henry

    From Heinrich Lenz, the physicist that created Lenz's Law we get inductance (L) which is represented in the derived unit of the Henry (H).

    The Henry (named after Joseph Henry) is 1 ampere (A) traveling through a flux linkage of 1 Weber (Wb) turn.

    The Weber / Ampere

    The Weber itself being a measure of mass multiplied by distance over time multiplied by amperes (Wb/A) is another standard unit inductance.

    How is inductance created?

    Two types of inductance exist:

    • Self-inductance occurs within a single coil of wire whether or not it is wrapped around a core.
    • Mutual inductance uses multiple coils and/or cores which creates a voltage change across both circuits.

    How Inductance Is Created

    Making a coil of wire creates a magnetic field which is described by inductance.

    The winding of the coil amplifies the current moving through with each coil effectively doubling the flow from the previous.

    So a single volt moving through a single loop becomes two volts and a second coil would create a total of three.

    Different types of current can be generated by different configurations of coils and cores.

    Magnetic (ferromagnetic) cores can oscillate or slide to create changes in the current being steady or transient.

    What is the inductance formula?

    The standard inductance formula is:

    v = L * Δi / Δt

    This represents that the voltage created is equal to a constant (L) multiplied by the time (t) rate of change in the current (i).

    In other words, inductance creates voltage through a ratio of current change. This gets described in inductance units of H.

    Self Inductance

    Self-inductance uses the above equation and is obviously easier to calculate than mutual-inductance as there are fewer variables.

    Remember that inductance takes place from wire to wire and coil to coil but can't be measured independently in each stage.

    The magnetic flux created cannot be parsed so a whole circuit must be measured.

    This is why sub equations created by James Clerk Maxwell exist to parse out each portion of the total circuit to understand how much inductance was created by each part.

    Using an inductance converter is a good way to make sense of the differences in micro and macro inductance.

    Inductance Across A Wire

    Working with an example of a straight wire we can calculate the inductance across the wire.

    To do this we understand that Ldc (where DC illustrates nanohenries) is equal to the length (l) of the wire multiplied by the radius (r) of the wire (to give us the total area of the circuit).

    Ldc = 2l * [ln (2l/r) - 0.75]

    Neumann Formula

    Mutual inductance becomes more complicated from the addition of the second set of wires and/or cores.

    For this, you have to calculate the area of both parts of the circuit as well as the interaction between.

    Lm,n = µ0/4π ∮ cm ∮ cn dxm · dxn / |xm - xn|

    This double integral inductance formula known as the Neumann formula takes into account the total curves of the wires (cm and cn) and also the permeability of the space (µ0).

    This gets further defined by the position of the wires (xm, xn) and their increments (dxm, dxn).

    How is inductance used?

    Self-inductance is used in chokes. Mutual-inductance is used in transformers.


    Inductance allows engineers to design circuits which can change and alter currents so that a single power source feeding a system can be used to a variety of things.

    Most modern electronics use a series of transformers and chokes to limit and manipulate voltage.

    Alarms and Triggers

    Inductance also makes it possible to send messages by chopping up current flow and releasing bursts in a controlled way.

    A fun and easy way to understand inductance use in the world can be done by the DIY crowd through inductive loop detectors.

    Many types of triggers and alarms use inductance loops to complete circuits and create force which can do work.

    Power Grids

    Generally, though, inductance principles make understanding power grids and a lot easier.

    For more science and engineering principles and their associated tools, check out our full list of physics calculators.

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