Magnetism -part II

We have many special case situations. Why special cases---Some of the expressions for finding "B" and for a Coulomb's law like expression are slightly more complicated when dealing with magnetic fields.

The simple case --GIVEN a uniform B fieldForce acting on MOVING charge in B field

Since the force due to the magnetic field is perpendicular to displacement(v) the work done by the magnetic force is zero.

UNITS: Solve our equation for B.

B=F/(qv)

Instead of N/C for E, or N/kg for g field, we have units of

Newtons/(Amp-meter) B

N/(A m) ---so and A m can be thought of as the source of mag field

1 Tesla=1N/(A m)

Notes 8 Mag fields II Page 1

So from the units--the basic building block of B fields can be thought

of as moving charges (qv) or a length of wire Am. I need to add a bunch of moving charges, or pieces of wire in some shape--to build a

real life source of B fields. The adding can be tricky here--so again, we do special cases

https://www.youtube.com/watch?v=xno5AZOlR8k

https://www.youtube.com/watch?v=slmV2IlluAM

https://www.ck12.org/physics/lorentz-force/lesson/Lorentz-Force-PPC/?referrer=concept_details

Practice problem. Given a magnetic field pointing into the page of 0.300T (a good size everyday magnet)--shoot an electron moving v=1.00x105m/s into the field at an angle of 45o to the field lines. What happens?

The electron beam is tilted down into -ish the page at 45 o .

Notes 8 Mag fields II Page 2

Notes 8 Mag fields II Page 3

The force is down toward bottom of the page--the resulting

motion is electrons do 2 things. 1) circle around the field lines (due to vperpendicular) 2) maintain a velocity vparallel since

there is no force in that direction.

Change perspective to see the motion--I'll try my best 3D

artwork.

What is the name for this shape (not a spiral)---but is called a ---c'mon bio majors---what is it……

Helix.

How big is the acceleration of the electron? Just use that F(magnetic) and the mass of electron. a=3.72x1015 m/s2 A lot of g's.

What is the radius of the helix. (must use vperp=v sin())

a=(vperp )2 /r………r=1.3 microns. (small)--we can make the circle part bigger by decreasing B or changing the speed.

Notes 8 Mag fields II Page 4

These two situationsare the same, except on the left, the charges are embedded in a wire. So theentire wire feels a force.

For the wire shown above, the force is to the right on the wire.DO YOUR RHR-1.

If the wire above carries 1.00A into a region with B=0.500T, and L=

1.00m

the force is

That is not a huge force, but what if I run the wire back again in a loop like this.

Notes 8 Mag fields II Page 5

Notes 8 Mag fields II Page 6

So if you place a current carrying wire so the current cuts across

magnetic field lines--then there is a force on the wire.

If I make "N" loops of wire then the force gets multiplied by N ---can we do something with that?

ALL ELECTRIC MOTORS AND GENERATORS ARE BASED UPON THIS

So we need to learn how to make a working motor (motor--not

motaur).

The wire loop of the simple motor has 4 sides I have labeled on each figure view. The sides 2,4 have zero force since they are parallel to the field lines. Even if they were not, there is no torque around the axis due to sides 2,4.

DO SIDES 1,3 HAVE A TORQUE THAT MAKES THE "MOTOR" ROTATE?

Wire 3 gets a F3 to the left, wire 1 gets a F1 equally --but to right.

Calculate the torque on the loop for this orientation (those wires poking into the eyeball--really run to a battery).

Notes 8 Mag fields II Page 7

Torque on the electric motor loop

Notes 8 Mag fields II Page 8

We picked the angle to look at that gives the maximum torque on this loop. The torque really depends on Angle between the normal to the loop---and the B field.

The magnetic dipole moment isHow big the "magnet-ness" of the loopis.

We still need a couple tricks to make this a functional motor. As angle goes from 90 to zero--this will peter out since no torque.

So, we need to make the current direction flip around over and over.

Using a split ring called a commutator on

the shaft with the wires ---we can flip the current direction in the loop to keep it

going.

For simple fun motor kits, just scraping varnish off half of the wire (tricky) is enough to keep the motor going.

Notes 8 Mag fields II Page 9

Magnets and copper plates ---watch thishttps://www.youtube.com/watch?v=sENgdSF8ppAMagnetic floating froghttps://www.youtube.com/watch?v=KlJsVqc0ywM

Kit motor videohttps://www.youtube.com/watch?v=8m6WenZQhhw

You notice that the kits have many coils (N) increasing the torque by

a factor of N. Real motors typically may have thousands of coils. So electric motors can be "drills", "washing machines", "tesla motors"

and so on.

Notes 8 Mag fields II Page 10

Colbert Digression:

Basic Force laws

Gravity

Electric

Magnetic

The sources are really part of a loop---to do the total force on a loop, I

need to do some vector adding, and need to understand the RHR directions--along with adding. We don't do. But look at how similar the

three force laws are. Constant, source 1, source 2/r^2.

Nature may not be easy, but it gives us the same kind of expression

over and over again.

Is it weird that the source for B is I*L ---? Sure, but we said that to begin with. Moving electric charge makes B. Or another way of saying that---CHANGING ELECTRIC FIELD CREATES MAGNETIC FIELD (TIED

TOGETHER)CHANGING MAGNETIC FIELDS MAKE/CREATE/ACCOMPANY--ELECTRIC

FIELD.

LET THERE BE LIGHT---REALLY---CHANGING E AND B IS LIGHT!!!!!!!!

Notes 8 Mag fields II Page 11

Special B fields

We have talked about force on moving charge in a given uniform B field, and also force on a current carrying wire in a given uniform B field

But, how do I make a specific geometry of B field.?

A long straight wire--What is the magnetic field due to a long straight current carrying wire?

For an "infinite" long straight current carrying wire, the B field lines are

concentric circles/"cans" wrapping around the current. This is useful for any wire we get close to--looks long and straight if close enough

While "staring" down the current, the field lines run CCW.

OR RHR2 Point the thumb of your right hand along the current---and wrap your fingers around it (in the way your fingers can bend). Your finger tips trace out the direction of the field lines, as the "wrap".

The field gets smaller as you get farther from the wire.

Notes 8 Mag fields II Page 12

Long straight wire formula

As you stare down current (coming into your eye) the Field lines wrap

CCW around the wire. RHR(2)

Other special cases: Force/length "between" two parallel long straight current carrying wires.

So, for a wire with current in the page pointing up---the field lines on the right of a wire point in, on the left point out. Note that there are three different regions here I (lines add up, out of page) , II (lines opposite), III (add up into page)

Notes 8 Mag fields II Page 13

For the two long straight parallel current carrying wires--right now--we are

concerned with "what is the force (per length) of one wire on the other"?

We can ask this in a better way--To calculate the force on say --wire one, we

need to know what the field DUE to wire 1 is at wire 2. What is the B field due to wire 1 and wire 2?

B1 at d=

Now to get the force on wire 2 at this position, I use F=BIL

Notes 8 Mag fields II Page 14

Force between long straight wires continued. Since we assume the wires

are very long, we can really only ask what the force is on a piece of the wire of length L. We divided L out on both sides to get

This makes sense, increasing either current makes the force larger, and

increasing d makes the force smaller.

What direction is the force? RHR 2---at wire 1, the field is into the page (for the current given). Now use RHR 1---Current points to top of page, field due to wire 1 into page (at wire 2), Force on wire 2 is toward wire 1--attractive. Like currents attract.

What if I have a simple set of numbers, two 1.00A currents placed 1.00m apart. Then

It is actually an experiment like this that is used to define the Coulomb (when such and such current flows each second, here is the observed force…)

To give bigger forces I just need to have multiple wires---can do most motors have thousands, and the elements are close together.

Also--magnets help

Notes 8 Mag fields II Page 15

Special case--current loop, and stacked current loop or coils

(SOLENOID)

First reexamine a single current loop

If I keep drawing---all the field lines cross the plane of the loop--and close on themselves---B field lines close!!!!!!!! (no monopoles=no place to start or stop)

On the inside of this loop, field lines INSIDE THE LOOP tend upward,

cutting across the plane of the loop upward. Field lines outside the loop cut across the plane of the loop downward. Edge on view.

We are going to take a bunch of these dipoles and stack them together. Or a spring like coil makes a really good approx to this.

Notes 8 Mag fields II Page 16

When I make a coil--SOLENOID---THE FIELD LINES STILL

POINT UP ON THE INSIDE, but there are more lines (more loops, more current, so more lines). The lines inside are all

crammed inside--tight packed. The lines outside are spread out.

A bunch of lines inside--

spread over small area. =STRONG FIELDAND UNIFORM

The same lines spread over ---how big an area ---outside? OH--almost infinite.B(outside) ~0.

So, to make a uniform field I just need to make a good coil of wire and run current through it.

Notes 8 Mag fields II Page 17

Can I add fields due to sources I have studied --say a couple wires --fields in region I,II,III--sure--lots of configurations YOU CAN DO

Yes--line up wires parallel to make a sheet---like pencils lined up on a table.

○

Is there a flat plate configuration?

Yes the number of lines tell me about "how much current".○

For E fields--the number of field lines told me about "how much

charge", is there something like that for Magnetism.?

Many more effects have to do with time dependence--that

means changing the current, or moving charge around, or changing B (or E) fields.

○

This is what is up next○

Changing B field is responsible for all power generation (really important--to you---Imagine taking away everything created using electricity from generators---

○

Oh, and change E & B define "electromagnetic

radiation"=light, radio waves, 5G, micro-waves, x-rays--you name it.

○

Some of the video's showed some weird stuff--like floating ---what gives.

Hang in there--really cool stuff coming up next.

Remaining open questions:

Notes 8 Mag fields II Page 18