Electromagnetic induction Presentation slide for courses, classes, lectures et al. Electromagnetic induction Chapter 21

INTRODUCTION TO INDUCTION 12/28/2018

Important Definition – Magnetic Flux Magnetic Field AREA Induction 12/28/2018

Induction 12/28/2018

The Essence of this Topic Consider a conductor that is shaped in a loop but is continuous. The conductor has a magnetic field through the loop that is not necessarily uniform. There is a MAGNETIC FLUX through this loop. If the FLUX CHANGES, an “emf” will be induced around the loop. This emf can cause a current to flow around the loop. Induction 12/28/2018

How Can You Change the Magnetic Flux Going Through The Loop? Huh? Divide the area of the loop into a very large number of small areas DA. Find the Magnetic Field through each area as well as the angle that it makes with the normal to the area. Compute the total flux through the loop. Induction 12/28/2018

The Magnetic Flux Going Through The Loop: Add up all of these pieces that are INSIDE the loop. Induction 12/28/2018

Changing F Change any or all of the And the Flux will change! Bi DAi fi Change the SHAPE of the loop Change the ANGLE that the loop makes with the magnetic field (subset of above) And the Flux will change! Induction 12/28/2018

WAIT A SECOND ……. You said that there is a conducting loop. You said that there is therefore a VOLTAGE or emf around the loop if the flux through the loop changes. But the beginning and end point of the loop are the same so how can there be a voltage difference around the loop? ‘tis a puzzlement! Induction 12/28/2018

REMEMBER when I said E Fields start and end on CHARGES??? DID I LIE?? Induction 12/28/2018

BUT WAIT, YOU STILL LIE! The truth Electric fields that are created by static charges must start on a (+) charge and end on a (–) charge as I said previously. Electric Fields created by changing magnetic fields can actually be shaped in loops. BUT WAIT, YOU STILL LIE! Induction 12/28/2018

Why do you STILL think I am a liar? Because you said that an emf is a voltage so if I put a voltmeter from one point on the loop around to the same point, I will get ZERO volts, won’t I Induction 12/28/2018

Yes … but this doesn’t make me a liar! Let Me Explain. Induction 12/28/2018

The POTENTIAL between two points Is the WORK that an external agent has to do to move a unit charge from one point to another. But we also have (neglecting the sign): Ds Induction 12/28/2018

So, consider the following: x x x x x x x E Conductor Induction 12/28/2018

How Big is the emf? Faraday’s Law Michael Faraday (1791-1867) Induction 12/28/2018

Q: Which way does E point? A: The way that you don’t want it to point! (Lenz’s Law) Induction 12/28/2018

OK. LET’S DO THE PHYSICS NOW Induction 12/28/2018

DEMOs Induction 12/28/2018

Is there an induced current??? Induction 12/28/2018

A changing magnetic field INDUCES a current in a circuit loop. Induction Effects A changing magnetic field INDUCES a current in a circuit loop.

Faraday’s Experiments ?

Insert Magnet into Coil

Remove Coil from Field Region

Summary

Does the Flux Change? 12/28/2018

Push a magnet into a coil of two wires and a current is produced via an emf. In this case, 2 coils, each has the SAME emf. Ohm’s Law still works, so Induction 12/28/2018

If we go from 2 to 4 coils, the current A Stays the same B Doubles C Is halved D Is four times larger Induction 12/28/2018

A rectangular circuit containing a resistor is perpendicular to a uniform magnetic field that starts out at 2.65 T and steadily decreases at 0.25 T/s. While this field is changing, what does the ammeter read? Induction 12/28/2018

••The conducting rod ab shown makes frictionless contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure. (a) Find the magnitude of the emf induced in the rod when it is moving toward the right with a speed 7.50 m/s. Induction 12/28/2018

Application: AC Voltage Generator Induction 12/28/2018

Almost DC Induction 12/28/2018

The Strange World of Dr. Lentz

Lenz’s Law Induced Magnetic Fields always FIGHT to stop what you are trying to do! i.e... Murphy’s Law for Magnets

Example of Nasty Lenz The induced magnetic field opposes the field that does the inducing!

Don’t Hurt Yourself! The current i induced in the loop has the direction such that the current’s magnetic field Bi opposes the change in the magnetic field B inducing the current.

Let’s do the Lentz Warp again !

Again: Lenz’s Law An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current. (The result of the negative sign that we always leave out!) … OR The toast will always fall buttered side down!

What Happens Here? Begin to move handle as shown. Assume a resistance R in the loop. Flux through the loop decreases. Current is induced which opposed this decrease – current tries to re- establish the B field.

What about a SOLID loop?? Eddy Currents Energy is LOST BRAKING SYSTEM METAL Pull Eddy Currents