Faraday's & Lenz's Laws

Currents make magnetic fields. Faraday asked the reverse question, and found that a changing magnetic field makes a current. This discovery powers every generator on Earth.

Faraday’s experiments#

Put a bar magnet on the axis of a wire loop connected to a galvanometer. Held still, nothing happens. Push the magnet toward the loop and the needle swings; pull it away and it swings the other way. The current lasts only while the magnet moves.

Faraday found the rule behind this and many similar experiments:

Φ is the magnetic flux, measured in webers (1 Wb = 1 T m²). It can change because B changes, because the loop’s area changes, or because the angle between them changes. The emf is the induced emf; in a loop of resistance R it drives an induced current:

Which way does the current go?#

Using the sign in Faraday’s law:

1. Put an arrow on the loop to choose a positive sense for current (any choice).
2. Curl your right-hand fingers along the arrow: the thumb gives the positive normal.
3. Find Φ with that normal. If Φ is increasing, ℰ is negative: the current flows against your arrow. If Φ is decreasing, it flows along it.

Lenz’s law#

A quicker way. The induced current makes its own magnetic field, which can strengthen or weaken the original flux. Nature always chooses:

• An N pole pushed toward a loop raises the flux; the induced current makes a field pointing back at the magnet, so the near face of the loop acts as an N pole and repels it.
• A sliding wire that shrinks a circuit in a field into the page lowers the flux; the induced current makes field into the page, i.e. it runs clockwise.
• A loop beside a straight wire whose current is increasing: the flux through the loop grows, so the induced current circulates to make field opposite to the wire’s.