1104/21/2304/21/23

Applied Physics

Lecture 15Lecture 15 Electricity and Magnetism

Induced voltages and induction Magnetic flux and induced emf Faraday’s law

Chapter 19-20

2204/21/2304/21/23

Chapter 20Chapter 20Induced EMF and InductionInduced EMF and Induction

3304/21/2304/21/23

20.1 Induced EMF and magnetic flux20.1 Induced EMF and magnetic flux

Just like in the case of electric flux, Just like in the case of electric flux, consider a situation where the magnetic consider a situation where the magnetic field is uniform in magnitude and field is uniform in magnitude and direction. Place a loop in the B-field.direction. Place a loop in the B-field.

The flux, The flux, , is defined as the product of , is defined as the product of the field magnitude by the area crossed the field magnitude by the area crossed by the field lines.by the field lines.

where is the component of B where is the component of B perpendicular to the loop, perpendicular to the loop, is the angle is the angle between B and the normal to the loop.between B and the normal to the loop.

Units: TUnits: T··mm22 or Webers (Wb) or Webers (Wb)

cosB A BA

Definition of Magnetic Flux

B

The value of magnetic flux is proportional to the total number of magnetic field lines passing through the loop.

4404/21/2304/21/23

A square loop 2.00m on a side is placed in a magnetic field of A square loop 2.00m on a side is placed in a magnetic field of strength 0.300T. If the field makes an angle of 50.0° with the strength 0.300T. If the field makes an angle of 50.0° with the normal to the plane of the loop, determine the magnetic flux normal to the plane of the loop, determine the magnetic flux through the loop. through the loop.

Problem: determining a fluxProblem: determining a flux

5504/21/2304/21/23

A square loop 2.00m on a side is placed in a magnetic field of strength 0.300T. If the field makes an angle of 50.0° with the normal to the plane of the loop, determine the magnetic flux through the loop.

Given:

L = 2.00 mB = 0.300 T = 50.0˚

Find:

=?

Solution:

From what we are given, we use

cosBA 2

2

0.300 2.00 cos50.0

0.386

T m

Tm

6604/21/2304/21/23

20.1 Induced EMF and magnetic flux20.1 Induced EMF and magnetic flux

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 goes and then goes back to its previous positionback to its previous position

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 when happens when the the switch is openedswitch is opened, except , except for the for the needle going in the needle going in the opposite directionopposite direction……

Picture © Molecular Expressions

Faraday’s experiment

What is going on?

7704/21/2304/21/23

20.2 Faraday’s law of induction20.2 Faraday’s law of induction

NSvI

Induced current

8804/21/2304/21/23

NSI

v

v

B

B

I

I

20.2 Faraday’s law of induction20.2 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.

9904/21/2304/21/23

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

AC Delco- +

1 volt

II(induced)

101004/21/2304/21/23

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

AC Delco- +

1 volt

I

111104/21/2304/21/23

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

AC Delco- +

1 volt

I(induced)

121204/21/2304/21/23

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

AC Delco- +

1 volt

NO!!

131304/21/2304/21/23

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

Bv

141404/21/2304/21/23

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

Bv

I

151504/21/2304/21/23

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

Bv

I

I

I

161604/21/2304/21/23

Faraday’s law of magnetic inductionFaraday’s law of magnetic induction

In all of those experiment induced EMF is caused by a change in the In all of those experiment induced EMF is caused by a change in the number of field lines through a loop. In other words,number of field lines through a loop. In other words,

The instantaneous EMF induced in a circuit equals the rate of change The instantaneous EMF induced in a circuit equals the rate of change of magnetic flux through the circuit.of magnetic flux through the circuit.

Lenz’s Law: Lenz’s Law: The polarity of the induced emf is such that it produces a The polarity of the induced emf is such that it produces a current whose magnetic field current whose magnetic field opposes the opposes the changechange in magnetic flux in magnetic flux through the loop. That is, the induced current tends to maintain the through the loop. That is, 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

171704/21/2304/21/23

Applications:Applications:

Ground fault interrupterGround fault interrupter

Electric guitarElectric guitar

Metal detectorMetal detector

……

181804/21/2304/21/23

Example : EMF in a loopExample : 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��������������

191904/21/2304/21/23

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

Given:

r = 0.30 mBi = 0.30 T Bf = -0.20 Tt = 1.5 s

Find:

EMF=?

The loop is always perpendicular to the field, so the normal to the loop is parallel to the field, so cos = 1. The flux is then

2BA B r

Initially the flux is

and after the field changes the flux is

2 20.30 0.30m =0.085 T mi T

2 20.20 0.30m =-0.057 T mf T

The magnitude of the average induced emf is:

2 20.085 T m -0.057 T m0.095

1.5f iemf V

t t s