1. Magnets, how do they work?
Magnetism Part I.
Magnets, how do they work?

2. Magnets and Magnetic Fields
Magnets have two ends – “poles” – called north and south.
Law of Poles: Like poles repel; unlike poles attract.

3. However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

4. Sources of Magnetism
Magnetic fields and forces come from moving charges
Most common sources of magnetism:
permanent magnets (bar, horseshoe, etc.)
electric current
In a permanent magnet, the magnetic field comes from the electron motions inside atoms (Domains)
In a current-carrying wire, the magnetic field arises because of the flow of charges

5. Magnetic Fields
A compass is used to measure the direction of a magnetic field
A compass is just a little bar magnet that can rotate
As you move a compass around a magnet it points in different directions
A magnetic field is defined as the entity that causes a compass needle to move

6. Magnetic fields can be visualized using magnetic field lines, which are always closed loops.

7. The Earth’s magnetic field is similar to that of a bar magnet.
The Earth’s “North Pole” is really a south magnetic pole, as the north ends of magnets are attracted to it.

8. A uniform magnetic field is constant in magnitude and direction.
The field between these two wide poles is nearly uniform.

9. Electricity and Magnetism
Electricity and magnetism are interconnected
Electric force and magnetic force are two aspects of the same force, called the electromagnetic force
“Electromagnetism” is the source of visible light, radio, microwaves, etc.

10. Electric Currents Produce Magnetic Fields
A current in a wire creates a magnetic field around it
The field lines are concentric circles around the wire
The right-hand rule tells us the direction of the B-field

11. A current-carrying loop of wire creates a magnetic field that looks like that of a bar magnet
B-field

12. A solenoid combines many loops of wire to create a strong magnetic field
The B-field inside the solenoid is uniform and strong
The B-field can be increased by inserting an iron rod, creating an electromagnet

13. Magnetism Part II.
Fields and Forces

14. Vector Directions
North
[Up]
West
[Left]
East
[Right]
South
[Down]

15. 3D Vectors! Down – towards the ground [Into the Page]
Up – towards the sky
[Out of the Page]

16. Force on an Electric Current in a Magnetic Field; Definition of B
A magnet exerts a force on a current-carrying wire. The direction of the force is given by a right-hand rule.

17. Right Hand Rule # 2
Using your right-hand:  point your thumb in the direction of the current, I
Point your other fingers in the direction of the magnetic field, B
Your palm now points in the direction of the magnetic force, Fmagnetic

18. 𝑭=𝑩𝑰𝑳 The force on the wire depends on I: The Current
L: The Length of the wire
B: The Magnetic Field (and its orientation θ)
𝐹=(𝐵 sin 𝜃 )𝐼𝐿, when θ=90°
𝑭=𝑩𝑰𝑳
This equation defines the magnetic field B.

19. Magnetic Field B (aka B-Field)
Unit of B: the tesla, T.
1 T = 1 N/A·m. (OMG 1 Tesla is HUGE!)
Another unit sometimes used: the gauss (G).
1 G = 10-4 T.

20. Example
A 1.61 x 103m straight, horizontal wire is located on the Earth’s equator and carries a current of 20.0A directed to the east. What is the magnitude and direction of the force exerted on the wire by the Earth’s magnetic field, which has a strength of 43.0μT?

21. Use the Right Hand Rule F = BIL = 43.0x10-6*20.0*1.61x103 = 1.38N
Up – towards the sky
[Out of the Page]

22. DEMO

23. Force between Two Parallel Wires
The magnetic field produced at the position of wire 2 due to the current in wire 1 is:
The force this field exerts on a length l2 of wire 2 is:
permeability of free space, μ0 = 4π × 10−7 N/A2

24. Two parallel current-carrying wires exert a force on each other
If I1 and I2 are in the same direction, they attract
If I1 and I2 are in opposite directions, they repel
The greater the currents, I1 and I2, the greater the force

25. Is it useful?
A galvanometer is the basic device inside analog ammeters and voltmeters

26. Force on Electric Charge Moving in a Magnetic Field
The force on a moving charge is related to the force on a current
𝐹=𝑞𝑣𝐵 sin 𝜃 , 𝑤ℎ𝑒𝑛 𝜃=90°
Once again, the direction is given by a right-hand rule. (Same rule - the thumb is now the velocity v)
𝑭=𝒒𝒗𝑩

27. What about negative charges?
The direction of the magnetic Force for a negative charge is the complete opposite
Use the Right Hand Rule and take the opposite of your final direction
(Or use the “Left Hand Rule”)

28. If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle.

29. Example
An Electron traveling to the right at 2.0x107 m/s enters a uniform magnetic field of T directed into the page. Describe its path quantitatively.
Mass of Electron: 9.1x10-31 kg
Charge of Electron: -1.6x10-19 C

30. The Electron moves in a circular path!
𝑭 = 𝒒𝒗𝑩 = 𝒎 𝒗 𝟐 𝒓
𝒓= 𝒎𝒗 𝒒𝑩 = 𝟗.𝟏× 𝟏𝟎 −𝟑𝟏 ∗𝟐.𝟎× 𝟏𝟎 𝟕 𝟏.𝟔× 𝟏𝟎 −𝟏𝟗 ∗𝟎.𝟎𝟏𝟎
=𝟏.𝟏× 𝟏𝟎 −𝟐 𝒎 𝒐𝒓 𝟏.𝟏𝒄𝒎
The path is a clockwise circular path

31. Summary

32. Electromagnetic Induction
Magnetism Part III.
Electromagnetic Induction

33. Review: Magnetism from Electricity
Remember that a current in a loop of wire creates a magnetic field:
The field lines “flow” through the loop of wire
The RHR tells us the direction of the field B
magnetic field
current-carrying loop of wire

34. Is it possible to create a current in a circuit using magnetism?
Almost 200 years ago, Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus:

35. He found no evidence when the current was steady, but did see a current induced when the switch was turned on or off.

36. DEMO

38. Therefore, a changing magnetic field induces an electromotive force.
Electromotive force (or emf) is an old fashioned name for potential difference
Some authors use emf when talking about the voltage induced in a conductor by a magnetic field
We will use Vind instead of emf for the symbol of induced voltage

39. Lenz’s Law
Which way will the induced current flow in the loop of wire?
Experiments show that the current in the loop always produces a field that opposes the motion
Lenz’s Law specifies the direction of the induced current:
The magnetic field of the induced current is in a direction to produce a field that opposes the change causing it

40. Theory of Induction
Imagine a moving segment of wire in a stationary magnetic field:
If the wire is moved to the right, positive charges in the wire will experience a force upward (negative downward)
This is an induced voltage along the wire! F
wire is moving this way B

41. The induced voltage (Vind) is proportional to the strength of the field (B), the length of wire in the field (L), and the velocity of the wire (v):
This equation is limited in usefulness because it involves just one piece of wire
We need to consider an entire loop of wire to see how moving it through a field will or will not induce a voltage
𝑽 𝒊𝒏𝒅 =𝑩𝒍𝒗

42. Experiments with a Loop
Faraday did many experiments with magnets and loops of wire and found several ways to induce a voltage:
moving the loop into or out of the field
making the loop rotate in the field
making the field stronger or weaker
changing the size of the loop
Faraday found a simple law that predicted and explained all of these results
He saw that each situation involved a change in what is called magnetic flux

43. A loop of wire defines an area:
Consider a magnetic field passing through the loop at an angle  from the normal
Magnetic flux (B) is a measure of the number of field lines that pass through the area at right angles to the area
area
loop of wire
normal B 

44. Magnetic Flux 𝚽 𝑩 =𝑨𝑩 cos 𝜽 A is the area of the loop
B is the magnetic field strength
 is the angle between the field and the loop
Unit of magnetic flux: weber, Wb.
1 Wb = 1 T·m2
𝚽 𝑩 =𝑨𝑩 cos 𝜽 A B 

45. Faraday’s Law of Induction
Faraday’s law of induction says that the magnitude of the induced voltage is equal to the rate of change of magnetic flux:
The direction of the induced voltage is such that the current in the loop creates a field that oppose the change (Lenz’s Law)
In practice, it is usually a coil of N loops rather than just one, so
𝑽 𝒊𝒏𝒅 = ∆ 𝚽 𝑩 ∆𝒕
𝑽 𝒊𝒏𝒅 =𝑵 ∆ 𝚽 𝑩 ∆𝒕

46. V Induced in a moving conductor

47. Example (#10 p. 739)
A Flexible loop of conducting wire has a radius of 0.12m and is perpendicular to a uniform magnetic field with a strength of 0.15T, as in Figure (a). The loop is grasped at opposite ends and is stretched until it closes to an area of 3.0x10-3 m2, as in Figure (b). If it takes 0.20s to close the loop, find the magnitude of the average induced voltage in the loop during this time.
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 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 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
Figure (a)
Figure (b)

48. 𝑽 𝒊𝒏𝒅 = ∆ 𝜱 𝑩 𝜟𝒕 ∆ 𝜱 𝑩 =𝑩 𝑨 𝒇 −𝑩 𝑨 𝒊 =𝑩 𝑨 𝒇 − 𝑨 𝒊
𝑽 𝒊𝒏𝒅 = ∆ 𝜱 𝑩 𝜟𝒕
∆ 𝜱 𝑩 =𝑩 𝑨 𝒇 −𝑩 𝑨 𝒊 =𝑩 𝑨 𝒇 − 𝑨 𝒊
|𝟎.𝟏𝟓 𝟎.𝟎𝟎𝟑𝟎−𝝅∗ 𝟎.𝟏𝟐 𝟐 |=𝟎.𝟎𝟎𝟔𝟑 𝑾𝒃
𝑽 𝒊𝒏𝒅 = 𝟎.𝟎𝟎𝟔𝟑 .𝟐𝟎 =𝟑.𝟐× 𝟏𝟎 −𝟐 𝑽