B. THE PUNCHLINE---WE WANT TO KNOW HOW TO …spots.augusta.edu/tcolbert/phys1112/SU2020/Module 9...So, how do we use Faraday's law to tell us the EMF (or induced voltage)? To generate

The law--when we get to it--relates changing magnetic field to induced EMF (electric potential, or "voltage").

•

If the currents are steady (not changing in time at any locations)

then the B field is steady

○

Magnetic field is made by moving electric charges--currents. •

How do you change B field?•

FARADAY'S LAW----

I change B at a location--by changing the currents. I can either dial up

bigger or smaller currents, or move the wires---magnets have little current loops inside (spins), so moving a magnet works to--at changing

B.

THE PUNCHLINE---WE WANT TO KNOW HOW TO CREATE/GENERATE/---AN ELECTRIC POTENTIAL DIFFERENCE (VOLTAGE, OR EMF)

I can use a battery---chemically created EMF ()1.I can build up static charge--this can be a big deal--van de graff

generators and others.

2.

OR--I CAN GIVE CHARGE A PUSH --BY HAVING CHARGE CROSS

MAGNETIC FIELD LINES.

3.

I DO NOT GET FREE ENERGY---I MUST PUT WORK IN--BUT ANYWAY

I CAN MAKE CHARGE CROSS FIELD LINES (OR FIELD LINES CROSS CHARGE)--PRODUCES EMF

Notes 9-Faradays Law Page 1

Consider two coils, one inside the other. (big slinky inside

little slinky).

Start with switch open. •

Build up may take micro or milli-seconds.○

Close switch--so now current builds up in primary coil•

The field lines were not here before○

The B field lines were made by turning the "electromagnet"

(current in primary) ON.

○

There are now field lines inside the primary coil---•

They were not here before. ○

Field lines swept across the wires making up the 2nd-ary coil.○

There are charges in that wire. When they move across field

lines (or vice-versa) there is a force---THEY MOVE.

○

The ones that are allowed to move--represent a 2nd-ary current AND EMF in the 2nd-ary coil

○

Some of those field lines are now inside the 2nd-ary coil.•

ONLY WHEN FIELD LINES ARE SWEEPING IN, OR OUT○

ONLY WHILST THINGS ARE CHANGING!!!!!!○

There is a reading on the voltmeter•

The effect is time dependent. The effect is only there when currents

are building up, or dying off (increasing or reducing…..changing) in the primary circuit.



Pictures of a loop in 2nd-ary coil at different times.

Before switch is closed1)

As switch is closed 2)The field is now building up to some max that may take a few milli-sec--field lines are due to primary coil--but some lines are inside the 2nd arycoil. The red lines are cutting across the black coil wire. During this time there isa reading on the voltmeter

The current in the primary has built3)up to maximum. Everything is static nowNo more additional lines cross the coil.There is no EMF now---wait, nothing changesno EMF still.

If you now open the switch again then the process will reverse --the picture is that field lines will spread out, cross the wire, and generate an (opposite) EMF

The EMF is only generated while field lines cross the wire.

ANOTHER PICTURE---ZOOM INTO PIECE OF 2ND-ARY COIL.

When closing the switchthe B lines moved inside the coil. Cutting across wire

If I am a charge (positive) sitting in the wire (conductor) then to me it

looks like field lines are coming toward me---this is the same as ME, the positive charge moving in the field. Recall what happened when charge moves in a B field (qvB ---force). These charges get pushed downward.



Pictures on the last couple pages---show us how charge gets

pushed around when either a field line crosses charge, or charge crosses a field line. Either way there is a push on the

charge that gives both a current and related EMF.

Wait--if the force is "qvB" and I am sitting on the charge, then the charge is not moving. So the magnetic force is zero. Hmmmm---Relativity--the field lines are moving. But I have two forces that act on charge, magnetic and electric. The force described IS NOT MAGNETIC--WE HAVE CREATED AN ELECTRIC FORCE BY MOVING B FIELD LINES!!!!!! (THERE IS AN EMF).

UH--I THOUGH THAT E FIELD=0 INSIDE CONDUCTORS--RIGHT, BUT ONLY FOR STATICS. WE ARE MOVING FIELD LINES.

I CAN DIAL UP/DOWN CURRENT ON MAGNET

OR I CAN PICK UP THE MAGNET AND

MOVE IT. IF YOU MEASURE A FORCE ON YOUR TEST CHARGE--AND RULE OUT OTHER FIELDS--THEN YOU KNOW I CHANGED "B"--EVEN ACROSS THE UNIVERSE.

THE EFFECT IS TRANSIENT.

So I now ask the question:Why did the field lines cross the wire?"To generate an EMF"!!!!!!!!!! LOL.


If I am adding some field lines to the area of the loop (magnetic flux) --at some rate--then I get an EMF just like there was a battery in the loop.

The Earth has a magnetic field--so if I just wave a metal rod across field

lines, that is like having a battery in the rod. YES

Charge gets pushed to top. It has no where to go--infinite resistance, so no steady current, but charge builds up (airplane wings--yup).


We need to keep looking at pictures and define some terms like "Magnetic Flux".

So, how do we use Faraday's law to tell us the EMF (or induced voltage)?

To generate an EMF in the loop, the number of field lines must be changing.

I need a better way to designate "number of field lines" (magnetic flux).

There are 3 ways to change the field lines inside that loop!

Change the field strength1)Change the area of the loop (stretchy wire? We can find ways)2)Change the orientation of the loop with respect to B field. 3)

First, let's define MAGNETIC FLUX so we know what we are talking

about changing (in a picture, magnetic flux counts field lines).

Magnetic Flux, or


Units for magnetic flux

BA has units of T m2 (recall T has units of N/(A m))…..

The Law--Faradays Law (and Lenz's law)

The induced EMF in a loop is proportional to the RATE OF CHANGE OF

MAGNETIC FLUX. And is in a direction to oppose the change that caused the EMF (meaning ---the change doesn't "want" to happen).

Two parts to this---How much EMF, and Which way (which way----the minus sign---is called Lenz's law).


Direction of induced EMF

Let's consider a simple loop in a changing B field.

I'll sketch three times.

So, as time passes I keep adding 3 field lines into the page.

That means B is increasing, or there is a B into the page. (We will reference the changing magnetic flux often)

There is a changing flux here (this picture) into the page.

The opposite of that (the induced flux---or induced field lines) is out of

the page.

There is an induced current that made the induced flux (induced field lines)---USE RHR 2

The direction of current is in direction of Induced EMF


You can get quick at this…..There are only a couple pictures. Looking from top down, induced current can be either CW or CCW. Change in flux can be either into loop or out. We

already have one picture.

What will decreasing the field do in the last picture?

Recall, I can change B (bigger OR SMALLER), I can change area--somehow, I can rotate loop. Rotating from the picture above will reduce flux (shown at maximum with field lines along normal).

Example: Given a loop with radius of 0.100m, the initial magnetic

field is 0.000T, and the field is ramped up to 0.200T in 1.00s. What is the EMF?

Cos()=1 here--normal out of page is in the direction of the field linesso the angle is zero.


Remember, the angle is between the normal and the field lines.

Discussion: Direction and Lenz's law

The field lines are increasing out of the page, into your eye--this is usually considered the positive "z" axis (pointing toward you). So x and y are in the plane of the page (x to the right, y toward top of paper). Angle, or rotation around the z axis is positive when CCW. Here we get a negative number. So the current is CW---

OK--I don't want to do that heavy thinking to get direction of induced EMF---We know induced B field (or opposite to the change in flux is INTO THE PAGE)

The Induced EMF here was small. Easy to crank up with 10,000 coils of wire looped together.

OK--you now have the basics of a generator--later we will do this for a rotating loop.


On that last example, Faraday's law gave us the induced EMF--and

direction. Can we find the current?--the induced current--sure, but we need the resistance of the loop.

We still have same Old Ohm's law

No, that can't happen--there are other limiting factors. I must do work to make that current--I can't do infinite work. Superconductors do exist though---with R=0.

So --if R is zero---will the current become infinite?

Are there other systems? Sure--we do a Motional EMF system---or as I like to call it, Rod on Rails. Let's just start with metal rod passing magnetic field lines.

We pull the rod (length L) to right at a speed v in a field into the page, B.The charges inside the rod get a force on them--and I can consider this as "qvB". As the positive charges get dragged to the right, there is a force on them, moving them either up or down. The charge gets pushed upward on this rod. But no place to go---


The charges build up due to magnetic push--

until and equal and opposite electric field in the wire pulls back (reaches equilibrium). Like a

battery--some charge sits at the top, ready and waiting.

If we assume that the induced Electric field inside the rod is uniform

and recall that |V|=|E L| (we had "d " before)

The induced EMF here was found by going all the way back to Forces (qE, and qvB), and taking it from there. We did not use Faradays law--but we can, we should, and we must get the same result. The above was an exercise to show you that work done by forces like qE, give the same result as --"Rate of Change of Flux".

To use Faraday's law on the above example, we change the picture slightly. Add rails (so you can see a loop--this is not needed, the EMF is there---but it's easier to see with a loop).



So, we have a metal rod--

rolling on metal rails forming a conducting loop

on the left.

Since the rod is rolling, the magnetic flux is increasing (inside the loop)

The rod has moved a distance x in a time t and in that time the flux in the left side has increased since the area containing B field has increased.

v is to the right (positive) B field is into page (negative), so EMF is positive CCW. (Positive charge goes upward in the rod as before).

Change in flux is into pageOpposite to that is out of pageUSE RHR 2 (fingers inside the loop wrap upward, thumb points

ccw).

Or we can use RHR 2----

No matter what the geometric set up is, move the loop, change the field, Faradays law works.


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B. THE PUNCHLINE---WE WANT TO KNOW HOW TO …spots.augusta.edu/tcolbert/phys1112/SU2020/Module 9...So, how do we use Faraday's law to tell us the EMF (or induced voltage)? To generate