- 152 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Induction' - josiah

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### The Strange World of Dr. Lentz

### Lenz’s Law

Magnetic Flux

For a CLOSED Surface we might expect this to be equal to some constant times the

enclosed poles … but there ain’t no such thing!

CLOSED SURFACE

Induction - Fall 2006

Consider the poor little capacitor…

i

i

?

CHARGING OR DISCHARGING …. HOW CAN CURRENT

FLOW THROUGH THE GAP

In a FIELD description??

Induction - Fall 2006

Induction - Fall 2006

Insert Magnet into Coil

Induction - Fall 2006

Remove Coil from Field Region

Induction - Fall 2006

Remember the Definition of TOTAL ELECTRIC FLUX through a CLOSED surface:

Induction - Fall 2006

Magnetic Flux

- Applies to an OPEN SURFACE only.
- “Quantity” of magnetism that goes through a surface.

surface

Induction - Fall 2006

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

Consider a Loop- Magnetic field passing through the loop is CHANGING.
- FLUX is changing.
- There must be an emf developed around the loop.
- A current develops (as we saw in demo)
- Work has to be done to move a charge completely around the loop.

Induction - Fall 2006

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

Faraday’s Law (Michael Faraday)- Again, for a current to flow around the circuit, there must be an emf.
- (An emf is a voltage)
- The voltage is found to increase as the rate of change of flux increases.

Induction - Fall 2006

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

Faraday’s Law (Michael Faraday)We will get to the minus sign in a short time.

Induction - Fall 2006

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

Faraday’s Law (The Minus Sign)Using the right hand rule, we

would expect the direction

of the current to be in the

direction of the arrow shown.

Induction - Fall 2006

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

Faraday’s Law (More on the Minus Sign)The minus sign means that the current goes the other way.

This current will produce a magnetic field that would be coming OUT of the page.

The Induced Current therefore creates a magnetic field that OPPOSES the attempt to INCREASE the magnetic field! This is referred to as Lenz’s Law.

Induction - Fall 2006

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

How much work?emf

Faraday's Law

A magnetic field and an electric field are

intimately connected.)

Induction - Fall 2006

Induction - Fall 2006

MAGNETIC FLUX

- This is an integral over an OPEN Surface.
- Magnetic Flux is a Scalar
- The UNIT of FLUX is the weber
- 1 weber = 1 T-m2

Induction - Fall 2006

Flux Can Change

- If B changes
- If the AREA of the loop changes
- Changes cause emf s and currents and consequently there are connections between E and B fields
- These are expressed in Maxwells Equations

Induction - Fall 2006

Three of Maxwell’s Four Equations(Next Course .. Just a Preview!)

Ampere’s Law

Gauss

Faraday

Induction - Fall 2006

The Flux into the page begins to increase.

An emf is induced around a loop

A current will flow

That current will create a new magnetic field.

THAT new field will change the magnetic flux.

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx

Another View Of That damned minus sign again …..SUPPOSE that B begins to INCREASE its MAGNITUDE INTO THE PAGEInduction - Fall 2006

Induced Magnetic Fields always FIGHT to stop what you are trying to do!

i.e... Murphy’s Law for Magnets

Induction - Fall 2006

Example of Nasty Lenz

The induced magnetic field opposes the

field that does the inducing!

Induction - Fall 2006

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.

Induction - Fall 2006

The toast will always fall buttered side down!

Lenz’s LawAn 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!) …

Induction - Fall 2006

An Example

- The field in the diagram
- creates a flux given by
- FB=6t2+7tin milliWebers
- and t is in seconds.
- What is the emf when
- t=2 seconds?
- (b) What is the direction
- of the current in the
- resistor R?

Induction - Fall 2006

This is an easy one …

Direction? B is out of the screen and increasing.

Current will produce a field INTO the paper

(LENZ). Therefore current goes clockwise and R

to left in the resistor.

Induction - Fall 2006

Figure 31-36 shows two parallel loops of wire having a common axis. The smaller loop (radius r) is above the larger loop (radius R) by a distance x >>R. Consequently, the magnetic field due to the currenti in the larger loop is nearly constant throughout the smaller loop. Suppose that x is increasing at the constant rate of dx/dt = v. (a) Determine the magnetic flux through the area bounded by the smaller loop as a function of x. (Hint: See Eq. 30-29.) In the smaller loop, find (b) the induced emf and (c) the direction of the induced current.

v

Induction - Fall 2006

B is assumed to be constant through the center of the small loop and caused by the large one.

Induction - Fall 2006

What Happens Here?

- Begin to move handle as shown.
- Flux through the loop decreases.
- Current is induced which opposed this decrease – current tries to re-establish the B field.

Induction - Fall 2006

moving the bar

Induction - Fall 2006

Definition

Current in loop produces a magnetic field

in the coil and consequently a magnetic flux.

If we attempt to change the current, an emf

will be induced in the loops which will tend to

oppose the change in current.

This this acts like a “resistor” for changes in current!

Induction - Fall 2006

Look at the following circuit:

- Switch is open
- NO current flows in the circuit.
- All is at peace!

Induction - Fall 2006

Close the circuit…

- After the circuit has been close for a long time, the current settles down.
- Since the current is constant, the flux through the coil is constant and there is no Emf.
- Current is simply E/R (Ohm’s Law)

Induction - Fall 2006

Close the circuit…

- When switch is first closed, current begins to flow rapidly.
- The flux through the inductor changes rapidly.
- An emf is created in the coil that opposes the increase in current.
- The net potential difference across the resistor is the battery emf opposed by the emf of the coil.

Induction - Fall 2006

Close the circuit…

Induction - Fall 2006

Moving right along …

Induction - Fall 2006

Definition of Inductance L

UNIT of Inductance = 1 henry = 1 T- m2/A

FB is the flux near the center of one of the coils

making the inductor

Induction - Fall 2006

Inductive Circuit

- Switch to “a”.
- Inductor seems like a short so current rises quickly.
- Field increases in L and reverse emf is generated.
- Eventually, i maxes out and back emf ceases.
- Steady State Current after this.

i

Induction - Fall 2006

THE BIG INDUCTION

- As we begin to increase the current in the coil
- The current in the first coil produces a magnetic field in the second coil
- Which tries to create a current which will reduce the field it is experiences
- And so resists the increase in current.

Lenz with an ATTITUDE!

Induction - Fall 2006

Solution

Induction - Fall 2006

Switch position “b”

Induction - Fall 2006

Induction - Fall 2006

IMPORTANT QUESTION

- Switch closes.
- No emf
- Current flows for a while
- It flows through R
- Energy is conserved (i2R)

WHERE DOES THE ENERGY COME FROM??

Induction - Fall 2006

+dq

+q

-q

For an answerReturn to the Big C- We move a charge dq from the (-) plate to the (+) one.
- The (-) plate becomes more (-)
- The (+) plate becomes more (+).
- dW=Fd=dq x E x d

Induction - Fall 2006

So …

Induction - Fall 2006

Induction - Fall 2006

IMPORTANT CONCLUSION

- A region of space that contains either a magnetic or an electric field contains electromagnetic energy.
- The energy density of either is proportional to the square of the field strength.

Induction - Fall 2006

Induction - Fall 2006

Download Presentation

Connecting to Server..