1. Magnetism B B B x x x x x x ® ® ® ® ® ­ ­ ­ ­ ­ ­ ­ ­ v v v ´ q q q F
The Magnetic Force B B B
x x x x x x
® ® ® ® ®
­ ­ ­ ­ ­ ­ ­ ­ v v v q q q F F
F = 0

2. Magnetism
Magnetic effects from natural magnets have been known for a long time. Recorded observations from the Greeks more than 2500 years ago.
The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece.
Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched.
Small sliver of lodestone suspended with a string will always align itself in a north-south direction—it detects the earth’s magnetic field.

3. Bar Magnet Bar magnet ... two poles: N and S
Like poles repel; Unlike poles attract.
Magnetic Field lines: (defined in same way as electric field lines, direction and density)
Does this remind you of a similar case in electrostatics?

4. Electric Field Lines of an Electric Dipole
Magnetic Field Lines of a bar magnet

5. Magnetic Monopoles N S N S
Perhaps there exist magnetic charges, just like electric charges. Such an entity would be called a magnetic monopole (having + or - magnetic charge).
How can you isolate this magnetic charge?
Try cutting a bar magnet in half: N S N S
Even an individual electron has a magnetic “dipole”!
Many searches for magnetic monopoles—the existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac)
No monopoles have ever been found:

6. Magnetic Fields
We know about the existence of magnetic fields by their effect on moving charges. The magnetic field exerts a force on the moving charge.
What is the "magnetic force"? How is it distinguished from the "electric" force?
a) magnitude: µ to velocity of q
b) direction: ^ to direction of q’s velocity
c) direction: ^ to direction of B
B is the magnetic field vector q F v
mag
Let’s start with some experimental observations about
the magnetic force:

7. r r r r B v q E F ´ + = Lorentz Force
• The force F on a charge q moving with velocity v through a region of space with electric field E and magnetic field B is given by: r r r r B v q E F + = F
x x x x x x v B q
® ® ® ® ®
F = 0
­ ­ ­ ­ ­ ­ ­ ­

8. Question Magnetic Force:
Three points are arranged in a uniform magnetic field. The B field points into the screen.
Magnetic Force:
A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is:
a) right b) left c) into the screen
d) out of the screen e) zero
If v = 0  F = 0.
The positive charge moves from point A toward B. The direction of the magnetic force on the particle is: If
then F = qvB
a) right b) left c) into the screen
d) out of the screen e) zero
If v is up, and B is into the page, then F is to the left.

9. Question: Magnetic Force:
The positive charge moves from point A toward C. The direction of the magnetic force on the particle is:
a) up and right b) up and left c) down and right
d) down and left
Magnetic Force:
If v is up and to the right, it is still perpendicular to B,
hence F = qvB then and F is up and to the left.

10. r r r F = q v ´ B Þ F = qvB sin Question q (a) F1 < F2 (b) F1 = F2
Two independent protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z-direction. Ignore the interaction between the two protons.
What is the relation between the magnitudes of the forces on the two protons? B x y z 1 2 v
(a) F1 < F2
(b) F1 = F2
(c) F1 > F2
The magnetic force is given by: r r r F = q v B Þ F =
qvB
sin q
In both cases the angle between v and B is 90°!!
Therefore F1 = F2.

11. Question (a) F2x < 0 (b) F2x = 0 (c) F2x > 0
Two independent protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z-direction. Ignore the interaction between the two protons.
What is F2x, the x-component of the force on the second proton? B x y z 1 2 v
(a) F2x < 0
(b) F2x = 0
(c) F2x > 0
To determine the direction of the force, we use the
right-hand rule.
As shown in the diagram, F2x < 0.

12. Question (a) decreases (b) increases (c) stays the same
Two protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z-direction. Ignore the interaction between the two protons.
Inside the B field, the speed of each proton: B x y z 1 2 v
(a) decreases
(b) increases
(c) stays the same
Although the proton does experience a force (which deflects it), this is always to Therefore, there is no possibility to do work, so kinetic energy is constant and is constant.

13. Trajectory in Constant B Field
Suppose charge q enters B-field with velocity v as shown below. What will be the path q follows? F v R
x x x x x x v B q
Force is always ^ to velocity and B. What is path?
Path will be circle. The magnetic force provides the centripetal force needed to keep the charge in its circular orbit. Calculate R:

14. Radius of Circular Orbit
x x x x x x v F B q R
Lorentz force:
qvB F =
centripetal acc: R v a 2 =
Newton's 2nd Law: ma F = Þ R v m
qvB 2 qB mv
This is an important result, with useful experimental consequences !

15. Question: What is the direction of the magnetic field in chamber 1?
The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure.
What is the direction of the magnetic field in chamber 1?
a) Up b) Down c) Left
d) Right e) Into page f) Out of page

16. Question What is the direction of the magnetic field in chamber 2?
a) Up b) Down c) Left
d) Right e) Into page f) Out of page

17. Question a) B1 > B2 b) B1 = B2 c) B1 < B2
Compare the magnitude of the magnetic field in chamber 1 to the magnitude of the magnetic field in chamber 2.
a) B1 > B2
b) B1 = B2
c) B1 < B2
The magnetic force is always perpendicular to v.
The force doesn’t change the magnitude of v, it
only changes the particle’s direction of motion.
The force gives rise to a centripetal acceleration.
The radius of curvature is given by:

18. Question (a) W1 < W (b) W1 = W (c) W1 > W Definition of work Lv
A proton, moving at speed v, enters a region of space which contains a constant B field in the -z-direction and is deflected as shown.
Another proton, moving at speed v1 = 2v, enters the same region of space and is deflected as shown. B v1
Compare the work done by the magnetic field (W for v, W1 for v1) to deflect the protons.
(a) W1 < W
(b) W1 = W
(c) W1 > W
The magnetic force is:
Therefore, the work done is ZERO in each case:
Definition of work

19. Charges in a conductor - current
Now you know how a single charged particle moves in a magnetic field, what about a group?
For a piece of a conductor we know there are dl I vd n A

20. Implications
To get the sum of a number of vectors - put them all head to tail and connect the initial (a) and final point (b). So b a
If the initial and final points are the same, the integral is zero!
That is, the net magnetic force on a closed current loop in a uniform magnetic field is zero!
BUT……..

21. Torque
Although the net magnetic force acting on a closed current loop in a uniform magnetic field is zero, the forces are not
In the same place, so there can be a net torque. F
Loop has length dimension a into the page
(and normal to B)
Loop has width b. A  B X F

22. Question
Each of the two turns of a circular loop of wire conductor (diameter 20 cm) carries a current of I = 2 amps. If it is placed in a magnetic field of 0.1 T at 450 to the plane of the loop, the torque is;
a) x10-4 N-m b) 44.6 x10-4 N-m c) 88. x10-4 N-m

23. The Hall Effect Which charges carry current?
Positive charges moving counterclockwise experience upward force
Upper plate at higher potential
Negative charges moving clockwise experience upward force
Upper plate at lower potential
Equilibrium between electrostatic & magnetic forces:
This type of experiment led to the discovery (E. Hall, 1879) that current in conductors is carried by negative charges (not always so in semiconductors).
Can be used as a B-sensor.