Aeon Flux Aeon Flux & The Right Hand Rule& The Right Hand Rule

Current In A WireCurrent In A Wire

As you saw in the lab…..As you saw in the lab…..

Current in a wire will create a circular Current in a wire will create a circular magnetic field.magnetic field.

The direction of the field depends on The direction of the field depends on the direction of the COVENTIONAL the direction of the COVENTIONAL CURRENT flow.CURRENT flow.

Current In A WireCurrent In A Wire

The 1st Right Hand Rule

Loop de LoopLoop de Loop

You also found that loops of wire have You also found that loops of wire have a distinct north and south pole.a distinct north and south pole.

This is because each circular field This is because each circular field adds to the next.adds to the next.

Loop de LoopLoop de Loop

Loop de LoopLoop de Loop

NorthSouth

The 2nd Right Hand Rule

Newton Steps InNewton Steps InAn electric current exerts a force on a An electric current exerts a force on a

magnet.magnet.

By Newton’s third law we expect a magnet to By Newton’s third law we expect a magnet to exert a force on a current carrying wire.exert a force on a current carrying wire.

Orested found that Orested found that a magnet exerts a force a magnet exerts a force on a current carrying wire.on a current carrying wire.

He found that He found that the direction of the force is the direction of the force is always perpendicular to the direction of the always perpendicular to the direction of the current and also to the direction of the current and also to the direction of the magnet field,magnet field, B. B.

B Happy!B Happy!

As you have seen, we’ve been eating up As you have seen, we’ve been eating up the alphabet when it comes to variable the alphabet when it comes to variable definitions.definitions.

It makes sense that the force a current It makes sense that the force a current carrying wire exerts is related to…carrying wire exerts is related to…

II current flow current flow

ll length of wire length of wire

We know that F is the force in Newtons.We know that F is the force in Newtons.

B Happy!B Happy!

The only thing missing is the intensity The only thing missing is the intensity or size of the magnetic field.or size of the magnetic field.

We need a new variableWe need a new variable

B field intensity. B field intensity.

It’s analogous to g, gravitational field It’s analogous to g, gravitational field strength, g.strength, g.

Friends of BilFriends of Bil

We typically re-write this to the form:We typically re-write this to the form:

F = BF = BI I ll

A Wee Bit of HistoryA Wee Bit of History

Remember Projectile motion?Remember Projectile motion?

Vx = V cos Vx = V cos θθ

Vy = V sin Vy = V sin θθ

To resolve the launch velocity into two To resolve the launch velocity into two components we did the sin cos thing.components we did the sin cos thing.

A Wee Bit of HistoryA Wee Bit of History

We also talked about gyroscopes and We also talked about gyroscopes and the idea that an object confined to a the idea that an object confined to a circular motion had a force vector circular motion had a force vector NORMAL to the plane of rotation.NORMAL to the plane of rotation.

I described the torque vector using I described the torque vector using three fingers on my right hand.three fingers on my right hand.

I did same thing with the spinning I did same thing with the spinning bowling balls.bowling balls.

Friends of Bil, At An Friends of Bil, At An AngleAngle

If we place a wire in a magnetic field If we place a wire in a magnetic field and then run some current through and then run some current through it the wire will experience a force.it the wire will experience a force.

This statement is a corollary to This statement is a corollary to Orsted’s statement.Orsted’s statement.

But what if the B field and the wire But what if the B field and the wire are not perpendicular?are not perpendicular?

Funny you should ask!Funny you should ask!

Friends of Bil, At An Friends of Bil, At An AngleAngle

B

Wire

I

θ

Friends of Bil, At An Friends of Bil, At An AngleAngle

B

Wire

I

θ

B sinθ

The only portion of the field that matters is theis what’s perpendicularto the wire.

F is going into the screen away from you

Friends of Bil, Standard Friends of Bil, Standard FormForm

We typically re-write it in this form:We typically re-write it in this form:

F = BsinF = BsinθθI I llBut it’s more properly written as a But it’s more properly written as a

cross product:cross product:

F = B F = B xx I I ll

B Happy!B Happy!

The magnitude The magnitude BB of the magnetic of the magnetic field at any point in space is defined field at any point in space is defined asas

F

Il sin

Current Length of wire

Angle between the wire and magnetic field

Magnitude of magnetic field

Force on current in a wire caused by a magnetic field

B

The magnitude The magnitude BB of the magnetic of the magnetic field at any point in space is defined field at any point in space is defined asas

Friends of BilFriends of Bil

The units of field intensity are the The units of field intensity are the TESLA (T), named for Nikola Tesla.TESLA (T), named for Nikola Tesla.

F F N N

II l l (A • m) (A • m)B (Tesla) =B (Tesla) = ==

A Sign of ConventionA Sign of Convention

N S

N

B

B B

S

Plane

Vector enters the plane

X’s and O’sX’s and O’s

Out of Screen Into Screen

Tip (point) of an arrow coming toward you as seen from the S.

Tail feathers of an arrow going away from you as seen from the N.

X’s and O’sX’s and O’s

Cross Products Revealed

B

I

F

The 3rd Right Hand Rule

Zip, Boom, Bah!Zip, Boom, Bah!

Since we now embrace the idea that Since we now embrace the idea that current current II in a wire will create a in a wire will create a magnetic field B, it doesn’t take a magnetic field B, it doesn’t take a big leap to think about what happens big leap to think about what happens if we shoot a charged particle into a if we shoot a charged particle into a magnetic field.magnetic field.

After all, isn’t current just a bunch of After all, isn’t current just a bunch of “moving” charges any way?“moving” charges any way?

Zip, Boom, Bah!Zip, Boom, Bah!

Consider a positive charge, qConsider a positive charge, q++

Since current Since current II is merely coulombs of is merely coulombs of charge flowing per second (Amps = C/s)charge flowing per second (Amps = C/s)…..…..

A coulomb is just the amount of charge or A coulomb is just the amount of charge or the number of q’s, isn’t it?the number of q’s, isn’t it?

So if So if II is flow rate, wouldn’t it make is flow rate, wouldn’t it make sense that some charge, qsense that some charge, q++, could move , could move at some velocity, v, acting like an amp?at some velocity, v, acting like an amp?

Sure!!!!!!!!!!!!!!!!!Sure!!!!!!!!!!!!!!!!!

Zip, Boom, Bah!Zip, Boom, Bah!

Since Since F = BIl F = BIl

And….And….

F F N N N N

I l I l (A • m) C • m (A • m) C • m

ss

B (Tesla) =B (Tesla) = == ==

Zip, Boom, Bah!Zip, Boom, Bah!

Perhaps we can come up with some Perhaps we can come up with some kind of arrangement of F, B, q and v kind of arrangement of F, B, q and v that ends up being equal to a Tesla.that ends up being equal to a Tesla.

Let’s just take a shot in the dark………Let’s just take a shot in the dark………

F = qvBF = qvB

Zip, Boom, BahZip, Boom, Bah

Then as always we need to test the unitsThen as always we need to test the units

F F N N N N

q v q v C • m C • m C • m C • m

ss

s s

It *#&@ worked!!!It *#&@ worked!!!

== ==B (Tesla) =B (Tesla) =

Zip, Boom, BahZip, Boom, Bah

Like the last go around, the angle that Like the last go around, the angle that the particle approaches the field is the particle approaches the field is important, like a ship sailing across important, like a ship sailing across the wind.the wind.

B

q+vθ

v┴

F F = qvBsinF = qvBsinθθ

F = qv F = qv xx B B

B

v

F

The 3rd Right Hand Rule

aka Fleming’s Right Hand Rule for + charges

Use the left hand for - charges

The Relationship to T.V.The Relationship to T.V.

X X X X X X

X X X X X X

X X X X X X

X X X X X X

X X X X X X

q0

q+

q-

Going In CirclesGoing In Circles

Since force F depends on charge Since force F depends on charge magnitude q and velocity v ……..magnitude q and velocity v ……..

It makes sense that under the right It makes sense that under the right conditions a charge can be injected conditions a charge can be injected into a field and enter a circular orbit into a field and enter a circular orbit in the field………in the field………

Like a ball on a sting!Like a ball on a sting!

Going In CirclesGoing In Circles

X X X X X X

X X X X X X

X X X X X X

X X X X X X

X X X X X XV

r

Way Back In OctoberWay Back In October

I showed you how we figured out orbital I showed you how we figured out orbital radius based on radius based on centripetal accelerationcentripetal acceleration..

We discussed this as part of Newton’s We discussed this as part of Newton’s Canon.Canon.

So we currently know these things…….So we currently know these things……. F=maF=ma 22ndnd Law Law F=BqvF=Bqv

aacc=v=v22/r/r centripetal acclerationcentripetal accleration

Last time we substituted aLast time we substituted acc into the 2 into the 2ndnd Law LawHere we go!Here we go!

Pardon My DerivationPardon My Derivation

ma = Bqvma = Bqv 22ndnd Law = Charge Law = Charge ForceForce

a = Bqv/ma = Bqv/m solve for asolve for a

vv22/r = Bqv/m/r = Bqv/m substitute asubstitute acc

r/vr/v22 = m/Bqv = m/Bqv setting up to solve for rsetting up to solve for r

r = mvr = mv22/Bqv/Bqv solving for rsolving for r

r =mv/Bqr =mv/BqSo let it be written, so let be done.So let it be written, so let be done.

““So What?”, You Ask?So What?”, You Ask?

X X X X X X

X X X X X X

X X X X X X

X X X X X X

X X X X X XStream of singly ionized Carbon atoms, q+

14 C

12 C

Radio Carbon Dating