Aeon Flux & The Right Hand Rule

1. Aeon Flux & The Right Hand Rule

2. Current In A Wire As you saw in the lab….. Current in a wire will create a circular magnetic field. The direction of the field depends on the direction of the COVENTIONAL CURRENT flow.

3. Current In A Wire The 1st Right Hand Rule

4. Loop de Loop You also found that loops of wire have a distinct north and south pole. This is because each circular field adds to the next.

5. Loop de Loop

6. Loop de Loop South North The 2nd Right Hand Rule

7. Newton Steps In An electric current exerts a force on a magnet. By Newton’s third law we expect a magnet to exert a force on a current carrying wire. Orested found that a magnet exerts a force on a current carrying wire. He found that the direction of the force is always perpendicular to the direction of the current and also to the direction of the magnet field, B.

8. B Happy! As you have seen, we’ve been eating up the alphabet when it comes to variable definitions. It makes sense that the force a current carrying wire exerts is related to… I current flow l length of wire We know that F is the force in Newtons.

9. B Happy! The only thing missing is the intensity or size of the magnetic field. We need a new variable B field intensity. It’s analogous to g, gravitational field strength, g.

10. Friends of Bil We typically re-write this to the form: F = BI l

11. A Wee Bit of History Remember Projectile motion? Vx = V cos θ Vy = V sin θ To resolve the launch velocity into two components we did the sin cos thing.

12. A Wee Bit of History We also talked about gyroscopes and the idea that an object confined to a circular motion had a force vector NORMAL to the plane of rotation. I described the torque vector using three fingers on my right hand. I did same thing with the spinning bowling balls.

13. Friends of Bil, At An Angle If we place a wire in a magnetic field and then run some current through it the wire will experience a force. This statement is a corollary to Orsted’s statement. But what if the B field and the wire are not perpendicular? Funny you should ask!

14. Friends of Bil, At An Angle I θ B Wire

15. Friends of Bil, At An Angle I B sinθ F is going into the screen away from you θ The only portion of the field that matters is the is what’s perpendicular to the wire. B Wire

16. Friends of Bil, Standard Form We typically re-write it in this form: F = BsinθI l But it’s more properly written as a cross product: F = B xI l

17. B Happy! The magnitude B of the magnetic field at any point in space is defined as The magnitude B of the magnetic field at any point in space is defined as Angle between the wire and magnetic field Force on current in a wire caused by a magnetic field F B Il sin q Magnitude of magnetic field Current Length of wire

18. Friends of Bil The units of field intensity are the TESLA (T), named for Nikola Tesla. F N I l (A • m) B (Tesla) = =

19. A Sign of Convention B B N S S B Plane N Vector enters the plane

20. X’s and O’s 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. Out of Screen Into Screen

21. X’s and O’s

22. Cross Products Revealed

23. The 3rd Right Hand Rule I B F

25. Zip, Boom, Bah! Since we now embrace the idea that current I in a wire will create a magnetic field B, it doesn’t take a big leap to think about what happens if we shoot a charged particle into a magnetic field. After all, isn’t current just a bunch of “moving” charges any way?

26. Zip, Boom, Bah! Consider a positive charge, q+ Since current I is merely coulombs of charge flowing per second (Amps = C/s)….. A coulomb is just the amount of charge or the number of q’s, isn’t it? So if I is flow rate, wouldn’t it make sense that some charge, q+, could move at some velocity, v, acting like an amp? Sure!!!!!!!!!!!!!!!!!

27. Zip, Boom, Bah! Since F = BIl And…. F N N I l (A • m) C • m s B (Tesla) = = =

28. Zip, Boom, Bah! Perhaps we can come up with some kind of arrangement of F, B, q and v that ends up being equal to a Tesla. Let’s just take a shot in the dark……… F = qvB

29. Zip, Boom, Bah Then as always we need to test the units F N N q v C • m C • m ss It *#&@ worked!!! = B (Tesla) = =

30. Zip, Boom, Bah Like the last go around, the angle that the particle approaches the field is important, like a ship sailing across the wind. F F = qvBsinθ F = qv x B v θ q+ v┴ B

31. The 3rd Right Hand Rule aka Fleming’s Right Hand Rule for + charges v B Use the left hand for - charges F

32. The Relationship to T.V. q+ 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-

33. Going In Circles Since force F depends on charge magnitude q and velocity v …….. It makes sense that under the right conditions a charge can be injected into a field and enter a circular orbit in the field……… Like a ball on a sting!

34. Going 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 X r V

35. Way Back In October I showed you how we figured out orbital radius based on centripetal acceleration. We discussed this as part of Newton’s Canon. So we currently know these things……. F=ma 2nd Law F=Bqv ac=v2/r centripetal accleration Last time we substituted ac into the 2nd Law Here we go!

36. Pardon My Derivation ma = Bqv 2nd Law = Charge Force a = Bqv/m solve for a v2/r = Bqv/m substitute ac r/v2 = m/Bqv setting up to solve for r r = mv2/Bqv solving for r r =mv/Bq So let it be written, so let be done.

37. “So What?”, You Ask? 14 C 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 12 C Radio Carbon Dating Stream of singly ionized Carbon atoms, q+