Chapter 3: Faraday’s Chapter 3: Faraday’s LawLaw

2.1 Induced EMF and magnetic 2.1 Induced EMF and magnetic fluxflux

Two circuits are not Two circuits are not connected: no current?connected: no current?

However, However, closing the switchclosing the switch we see that the compass’ we see that the compass’ needle needle movesmoves and then and then goes back to its previous goes back to its previous positionposition

Nothing happensNothing happens when the when the currentcurrent in the primary coil is in the primary coil is steadysteady

But But same thingsame thing happens happens when the when the switch is openedswitch is opened, , except for the except for the needle going needle going in the opposite directionin the opposite direction……

Picture © Molecular Expressions

Faraday’s experiment

What is going on?

2.2 Faraday’s law of induction2.2 Faraday’s law of induction

NSvI

Induced current

NSI

v

v

B

B

I

I

2.2 Faraday’s law of induction2.2 Faraday’s law of induction

A current is set up in the circuit as long as there is relative motion between the magnet and the loop.

Does there have to be motion?Does there have to be motion?

AC Delco- +

1 volt

II(induced)

Does there have to be motion?Does there have to be motion?

AC Delco- +

1 volt

I

Does there have to be motion?Does there have to be motion?

AC Delco- +

1 volt

I(induced)

Does there have to be motion?Does there have to be motion?

AC Delco- +

1 volt

NO!!

Maybe the B-field needs to Maybe the B-field needs to change…..change…..

Bv

Maybe the B-field needs to Maybe the B-field needs to change…..change…..

Bv

I

Maybe the B-field needs to Maybe the B-field needs to change…..change…..

Bv

I

I

I

Faraday’s law of magnetic Faraday’s law of magnetic inductioninduction

In all of those experiment induced EMF is In all of those experiment induced EMF is caused by a change in the number of field caused by a change in the number of field lines through a loop. In other words,lines through a loop. In other words,The instantaneous EMF induced in a The instantaneous EMF induced in a circuit equals the circuit equals the rate of change of rate of change of magnetic fluxmagnetic flux through the circuit. through the circuit.

Lenz’s LawLenz’s Law: The polarity of the induced : The polarity of the induced

emf is such that it produces a current emf is such that it produces a current whose magnetic fieldwhose magnetic field opposes the opposes the changechange in magnetic fluxin magnetic flux through the loop. That is, through the loop. That is, the induced current tends to maintain the the induced current tends to maintain the original flux through the circuit. original flux through the circuit.

Nt

E

Lenz’s law

The number of loops matters

Applications:Applications: Ground fault Ground fault

interrupterinterrupter Electric guitarElectric guitar SIDS monitorSIDS monitor Metal detectorMetal detector ……

Example 1: EMF in a loopExample 1: EMF in a loop

A wire loop of radius 0.30m lies so that an external magnetic field A wire loop of radius 0.30m lies so that an external magnetic field of strength +0.30T is perpendicular to the loop. The field changes of strength +0.30T is perpendicular to the loop. The field changes to -0.20T in 1.5s. (The plus and minus signs here refer to opposite to -0.20T in 1.5s. (The plus and minus signs here refer to opposite directions through the loop.) Find the magnitude of the average directions through the loop.) Find the magnitude of the average induced emf in the loop during this time. induced emf in the loop during this time.

B--------------

Example 2: EMF of a flexible Example 2: EMF of a flexible looploop

The flexible loop in figure below has a radius of 12cm and is in a magnetic The flexible loop in figure below has a radius of 12cm and is in a magnetic field of strength 0.15T. The loop is grasped at points A and B and field of strength 0.15T. The loop is grasped at points A and B and stretched until it closes. If it takes 0.20s to close the loop, find the stretched until it closes. If it takes 0.20s to close the loop, find the magnitude of the average induced emfmagnitude of the average induced emf in it during this time. in it during this time.

X X X X

X X X X

X X X X

X X X X

A

B

2.3 Motional EMF2.3 Motional EMF

Bv

Let's consider a conducting bar moving perpendicular to a uniform Let's consider a conducting bar moving perpendicular to a uniform magnetic field with constant velocity v. magnetic field with constant velocity v.

This force will act on free charges in the conductor. It will tend to move negative charge to one end, and leave the other end of the bar with a net positive charge.

sinF qvB

F

l

Motional EMFMotional EMF The separated charges will create an electric field The separated charges will create an electric field

which will tend to pull the charges back together. which will tend to pull the charges back together. When equilibrium exists, the magnetic force,When equilibrium exists, the magnetic force,

F=qvBF=qvB, will balance the electric force, , will balance the electric force, F=qEF=qE,, such such that a free charge in the bar will feel no net force. that a free charge in the bar will feel no net force.

Thus, at equilibrium, Thus, at equilibrium, E = vBE = vB.. The potential The potential difference across the ends of the bar is given by difference across the ends of the bar is given by V=ElV=El oror

A potential difference is maintained across the A potential difference is maintained across the conductor as long as there is motion through the conductor as long as there is motion through the field. If the motion is reversed, the polarity of the field. If the motion is reversed, the polarity of the potential difference is also reversed. potential difference is also reversed.

V El Blv

Motional EMF – conducting railsMotional EMF – conducting rails

Bv

We can apply Faraday's law to the complete loop. The change of flux through We can apply Faraday's law to the complete loop. The change of flux through the loop is proportional to the change of area from the motion of the bar:the loop is proportional to the change of area from the motion of the bar:

BA Bl x xBl Blv

t t

Eor (Faraday’s law)

BlvI

R R

Ecurrent Motional EMF

x

R

Example: wire in the magnetic Example: wire in the magnetic fieldfield

Over a region where the vertical component of the Earth's magnetic field is Over a region where the vertical component of the Earth's magnetic field is 40.0µT directed downward, a 5.00 m length of wire is held in an east-west 40.0µT directed downward, a 5.00 m length of wire is held in an east-west direction and moved horizontally to the north with a speed of 10.0 m/s. direction and moved horizontally to the north with a speed of 10.0 m/s. Calculate the potential difference between the ends of the wire, and Calculate the potential difference between the ends of the wire, and determine which end is positive. determine which end is positive.

2.4 Lenz’s law revisited2.4 Lenz’s law revisited

Lenz's law says that the induced current will Lenz's law says that the induced current will produce magnetic flux produce magnetic flux opposing this changeopposing this change. To . To oppose an increase into the page, it generates oppose an increase into the page, it generates magnetic field which points out of the page, at magnetic field which points out of the page, at least in the interior of the loop. Such a magnetic least in the interior of the loop. Such a magnetic field is produced by a field is produced by a counterclockwisecounterclockwise current current (use the right hand rule to verify). (use the right hand rule to verify).

Application of Lenz's law will tell Application of Lenz's law will tell us the direction of induced us the direction of induced

currents, the direction of currents, the direction of applied or applied or produced forces, produced forces, and the polarity and the polarity of induced of induced emf's.emf's.

Lenz’s law: energy conservationLenz’s law: energy conservation We arrive at the same conclusion from We arrive at the same conclusion from

energy conservation point of viewenergy conservation point of view The preceding analysis found that the The preceding analysis found that the

current is moving ccw. Suppose that this current is moving ccw. Suppose that this is not so.is not so.– If the current If the current I I is cw, the direction of is cw, the direction of

the magnetic force, the magnetic force, BlIBlI, on the sliding , on the sliding bar would be bar would be rightright..

– This would accelerate the bar to the This would accelerate the bar to the right, increasing the area of the loop right, increasing the area of the loop even more.even more.

– This would produce even greater force This would produce even greater force and so on.and so on.

– In effect, this would generate energy In effect, this would generate energy out of nothing violating the law of out of nothing violating the law of conservation of energy. conservation of energy.

Our original Our original assertion that the assertion that the current is cw is current is cw is not right, so the not right, so the current is ccw!current is ccw!

N

S

N

SS

N

S

v v

change change

The induced flux seeks to counteract the change.

Example: direction of the Example: direction of the currentcurrent

Find the direction of the current induced in the resistor at the instant the switch is closed.

Applications of Magnetic InductionApplications of Magnetic Induction Tape / Hard Drive / ZIP ReadoutTape / Hard Drive / ZIP Readout

– Tiny coil responds to change in flux as the magnetic domains Tiny coil responds to change in flux as the magnetic domains (encoding 0’s or 1’s) go by.(encoding 0’s or 1’s) go by.

Question: How can your VCR display an image while paused?Question: How can your VCR display an image while paused?

Credit Card ReaderCredit Card Reader– Must swipe cardMust swipe card generates changing fluxgenerates changing flux– Faster swipe Faster swipe bigger signal bigger signal