Magnetic & Electric Field Relationships

What is a Magnetic Field

Magnetic Field Generation

Magnetic and Electric Field Relationships

Important Uses


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The Relationship Between Magnetic and Electric Fields

Faraday's Law

When a magnet moves through a conducting coil, it generates a changing magnetic field, which creates a concurrent electric field (driving current in the coil.) This relationship is known as Faraday's Law, and the properties therein are the basis of many electrical generators and motors.

To describe Faraday's Law with mathematics:

E is the electromotive force (or EMF, the voltage around a closed loop), and Φm is the magnetic flux. The magnetic flux is further defined as the product of the area times the magnetic field normal to that area. This is why B is often also referred to as "magnetic flux density".

The negative sign represents Lenz' Law. Lenz' Law refers to the fact that any current generated by a changing magnetic field in a coil produces a magnetic field that opposes the change in the magnetic field that induced it.

Magnetic Fields Due to Changing Electric Fields

A changing electric force will generate a magnetic field, the same way that a changing magnetic field will generate an electric field. This physics fact is defined in "Maxwell's Correction to Ampere's Law". When Maxwell's correction is paired with Faraday's Law, it forms electromagnetic waves, such as light waves. Thus the cycle continues: a changing electric field generates a changing magnetic field which generates a changing electric field again. And so on, and so on.

Maxwell's correction is applied to Ampere's law as an additive term that is proportional to the time rate of change of the electric flux. It is similar to Faraday's Law, but with a different and positive constant out front.

The full Ampere Law then becomes the Maxwell-Ampere equation, which has such a small effect that it can be typically ignored in most cases where integral form is applied. The Maxwell term is, however, critical to the creation and propagation of electromagnetic waves, but these are usually described using alternate equations and go into deeper explanations than this website is intended for.

Therefore, electric and magnetic fields are different aspects of the same phenomenon.

As defined in the special theory of relativity, the division of the electromagnetic force into separate magnetic and electric components is not fundamental. It also depends on the perception of electric force as seen by the observer, versus what is seen by a second observer in a different frame of reference.

The special theory of relativity combines electric and magnetic fields into what's called the electromagnetic tensor. Changing reference frames mixes thes components, just like the way special relativity mixes space and time into spacetime. It's also the same theory as combining mass, momentum, and energy into four-momentum.

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