'Month of Equations': What Does Faraday's Law Really Mean?

October 29: The Maxwell Faraday Equation Meaning of Equation:

A changing magnetic flux through a closed circuit will produce an electromotive force in that circuit.

Considered as one of the most important equation that changed the course of history, the Maxwell Faraday is equation is a differential equation that relates that beautifully relates the changing magnetic flux with the electric field. There are many reasons why this equation was important to the world. But before that, let us understand what this really means. The Magnetic Flux is the number of field lines crossing through the unit surface.

Electricity and magnetism were two different branches of physics. It was later discovered that both are interconnected deeply. The first clue was from the Oersted's experiment in which a magnetic needle of a compass deflects when placed near a current carrying wire. Faraday did a lot of research in the field of magnetism, especially on electromagnets.  By this time, he knew that electricity can be used to produce magnetism, as in a solenoid. So he performed an experiment, expecting something. His experiment appeared something like this. The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G). He saw the transient current when he connected the wire to the battery, and another when he disconnected it.

Faraday explained his discovery with the concept of field lines. But no one believed him. Remember, Faraday was not a rigorous mathematician or a physicist. He worked as a laboratory assistant, aloof of the so called formal approach to proving something in physics by using mathematics. No one but James Maxwell took Faraday seriously. Maxwell was a top rate theoretical physicist. He was younger than Faraday and regarded him. He was also the one to prove Faraday's hypothesis that light is an electromagnetic wave.

From Faraday's experiment, it was clear that the changing magnetic flux (no. of magnetic field lines) is what induces an electromotive force along a closed path (electric circuit). This flux rule works in both directions. The result will be the same if you keep the loop stationary and change the flux by moving the magnet itself, or if you keep the magnet stationary and move the loop itself.

Faraday's law changed the course of human history. It is the fundamental principle of transformers, electric motors, generators and solenoids. This is one of the reason why Michael Faraday is also known as the "Architect of the Modern World".

To Read all the posts of the "Month of Equations" series, click here.