Conclusion – Chapter 20 & Chapter 21 – Electromagnetic induction Presentation slide for courses, classes, lectures et al. Chapter 21

Quick Review IB r Magnetism

Force Between Two Current Carrying Conductors First wire produces a magnetic field at the second wire position. The second wire therefore feels a force = Bil Magnetism

Solenoid B=~0 outside Magnetism

The Toroid– B=0 outside Magnetism

A rectangular loop has sides of length 0. 06 m and 0. 08 m A rectangular loop has sides of length 0.06 m and 0.08 m. The wire carries a current of 10 A in the direction shown. The loop is in a uniform magnetic field of magnitude 0.2 T and directed in the positive x direction. What is the magnitude of the torque on the loop? 8 × 10–3 N × m Magnetism

A solenoid of length 0. 250 m and radius 0 A solenoid of length 0.250 m and radius 0.0250 m is comprised of 440 turns of wire. Determine the magnitude of the magnetic field at the center of the solenoid when it carries a current of 12.0 A. 2.21 × 10–3 T Magnetism

The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin? 3 × 10–6 T Magnetism

Moving On to the next chapter………………. Magnetism

INTRODUCTION TO INDUCTION 4/16/2017

Important Definition – Magnetic Flux Magnetic Field AREA Induction 4/16/2017

Induction 4/16/2017

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 4/16/2017

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 4/16/2017

The Magnetic Flux Going Through The Loop: Add up all of these pieces that are INSIDE the loop. Induction 4/16/2017

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 4/16/2017

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 4/16/2017

Induction 4/16/2017

REMEMBER when I said E Fields start and end on CHARGES??? DID I LIE?? Induction 4/16/2017

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 4/16/2017

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 4/16/2017

Yes … but this doesn’t make me a liar! Let Me Explain. Induction 4/16/2017

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 4/16/2017

So, consider the following: x x x x x x x E Conductor Induction 4/16/2017

THEREFORE WHAT WILL A VOLTMETER READ FROM A to A? x x x x x x x A The emf B Zero C Can’t tell E  A Conductor Induction 4/16/2017

How Big is the emf? Faraday’s Law Michael Faraday (1791-1867) MINUS???? Induction 4/16/2017

Q: Which way does E point? A: The way that you don’t want it to point! (Lenz’s Law). Lenz’s Law Explains the (-) sign! Induction 4/16/2017

OK. LET’S DO THE PHYSICS NOW Induction 4/16/2017

DEMOs Induction 4/16/2017

Is there an induced current??? Induction 4/16/2017

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? 4/16/2017

In the Previous Example, if there are N coils rather than a single coil, A The current is increased by a factor of N B The current is decreased by a factor of N C The current stays the same. Induction 4/16/2017

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 4/16/2017

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 4/16/2017

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 4/16/2017

••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 4/16/2017

Application: AC Voltage Generator Induction 4/16/2017

Almost DC Induction 4/16/2017

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

The current in winding A is directed A cardboard tube is wrapped with two windings of insulated wire, as shown. Is the induced current in the resistor R directed from left to right or from right to left in the following circumstances? The current in winding A is directed (a) from a to b and is increasing, (b) from b to a and is decreasing, (c) from b to a and is increasing, and (d) from b to a and is constant. left right Induction 4/16/2017

Mutual inductance – Suppose i1 CHANGES Flux Changes Circulation of currents in one coil can generate a field in the coil that will extend to a second, close by device. Suppose i1 CHANGES Current (emf) is induced in 2nd coil.

The two coils Remember – the magnetic field outside of the solenoid is pretty much zero. Two fluxes (fluxi?) are the same! Induction 4/16/2017

Self-inductance – Any circuit which carries a varying current self-induced from it’s own magnetic field is said to have INDUCTANCE (L).

An inductor resists CHANGES in the current going through it. Induction 4/16/2017

An inductor resists CHANGES in the current going through it. Induction 4/16/2017

An inductor resists CHANGES in the current going through it. Induction 4/16/2017

Faraday says this is the emf! Inductance Defined If the FLUX changes a but during a short time Dt, then the current will change by a small amount Di. Faraday says this is the emf! This is actually a calculus equation Induction 4/16/2017

So … E= The UNIT of “Inductance – L” of a coil is the henry. SYMBOL: There should be a (-) sign but we use Lenz’s Law instead! The UNIT of “Inductance – L” of a coil is the henry. SYMBOL: Induction 4/16/2017

Induction 4/16/2017

Consider “AC” voltage Minimum Change/Dt V1 Maximum Change/Dt Induction 4/16/2017

FLUX is the same through The transformer FLUX is the same through both coils (windings). Induction 4/16/2017

Induction 4/16/2017

Induction 4/16/2017

Input/Output Impedance (Resistance) Induction 4/16/2017

Read in the textbook section 21.10: Induction 4/16/2017

Energy associated with an induced current. As energy is introduced at induces a field, energy is stored in an electronic device. Refer to worked example 21.12 in your text.

The R-L circuit – Figure 21.29 When an inductor is part of a wired circuit, - voltages, currents and capacitor charges are a function of time, not constants. Refer to worked example 21.13 in your text.

The L-C circuit – Figure 21.34 When an inductor is part of a wired circuit with a capacitor, the capacitor charges over time. Commonly used in radio as a tuner for the induced current from an antenna.