PHY C23: Lenz’s Law & further explanations on EM Induction

…and now we get to the exciting part!

  • Explanation on EM Induction
  • Lenz’s Law

Why is an e.m.f. generated when there is a change in magnetic flux?
It actually can be explained using the motor effect!

Consider a wire moving in a uniform magnetic field like so:

We can consider the effect on positive charges or negative charges.
Although it is really the electrons that move, conventional current follows positive charges.

So, let’s consider the positive charges.
If the wire moves to the right, we can see that positive charges ALSO move to the right.

Since current is the flow of positive charge, we can say that there is a current to the right:
Looks familiar?

We can use Fleming’s LEFT hand rule to deduce that there will be a force produced on the positive charges via the motor effect.

This force acts INTO the page & wants to PUSH positive charges INTO the page.
Hence, a CURRENT is induced:
We can use Fleming’s RIGHT hand rule as a shortcut to reach the same conclusion: current will flow into the page!
This explanation works with negative charges (electrons) as well.

Try it yourself – the final conclusion will still be that current flows into the page.

Fleming’s Right Hand Rule can be used to identify the direction of induced e.m.f. & current for simple setups.


There is one final law we must learn, but before that, let’s do another experiment:

You push a magnet perpendicularly into neutral, conducting coil. A current is generated… but in which direction?

Imagine we don’t know about Fleming’s Right Hand Rule or the motor effect. Can we still deduce the direction of induced current?

Here are the 2 options:

Option A
The changing magnetic flux induces a current as shown.

The current in the coil in turn induces a magnetic field:

This magnetic field REPELS the magnet.

To induce more current, you have to do work to push the magnet further in against the magnetic repulsion force.

So,
Energy you put in against the repulsion is converted to electrical energy in the coil.
Option B

The changing magnetic flux induces a current as shown.

The current in the coil in turn induces a magnetic field:

This magnetic field ATTRACTS the magnet.

The magnet is attracted into the coil.
More current is induced, which again induces a stronger magnetic field.
The magnet is attracted even stronger into the coil.
Even more current is induced, which induces a stronger magnetic field…

You have to do no work to induce a current.
In fact, you do NEGATIVE work, getting free energy out of nothing.

Not only does this create an impressive projectile weapon, it also disobeys the conservation of energy.

As you can see, Option A is correct while Option B is not true.
We can use the conservation of energy this way to prove our last law:


Lenz’s Law

Any induced e.m.f. will be established in a direction so as to produce effects which oppose the change that is producing it.

  1. Identify the polarity of any magnetic field that is needed to oppose the change
    • If a North pole is moving away from a coil, a South pole must face it to attract it back
    • If a North pole is moving towards a coil, a North pole must face it to repel it away
    • If a South pole is moving away from a coil, a North pole must face it to attract it back
    • If a South pole is moving towards a coil, a South pole must face it to repel it away
  2. Using Fleming’s Left Hand Rule, identify the direction of current required to produce this magnetic field via the motor effect

Finally, combining Faraday’s Law & Lenz’s Law in a single equation gives us:

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s