1. Objectives: After completing this module, you should be able to:
Define the magnetic field, discussing magnetic poles and flux lines.
Solve problems involving the magnitude and direction of forces on charges moving in a magnetic field.
Solve problems involving the magnitude and direction of forces on current carrying conductors in a B-field.

2. Magnetism
Since ancient times, certain materials, called magnets, have been known to have the property of attracting tiny pieces of metal. This attractive property is called magnetism. N S
Bar Magnet N S

3. Magnetic Poles S N
Iron filings
The strength of a magnet is concentrated at the ends, called north and south “poles” of the magnet. N S E W
Compass
Bar magnet
A suspended magnet: N-seeking end and S-seeking end are N and S poles.

4. Magnetic Attraction-Repulsion
Magnetic Forces: Like Poles Repel
Unlike Poles Attract

5. Magnetic Field Lines
We can describe magnetic field lines by imagining a tiny compass placed at nearby points. N S
The direction of the magnetic field B at any point is the same as the direction indicated by this compass.
Field B is strong where lines are dense and weak where lines are sparse.

6. Field Lines Between Magnets
Unlike poles N S
Attraction
Leave N and enter S N
Repulsion
Like poles

7. The Density of Field LinesDN
Line density DA
Electric field Df
Line density DA
Magnetic field flux lines f N S
Magnetic Field B is sometimes called the flux density in Webers per square meter (Wb/m2).

8. Magnetic Flux Density Df DA
Magnetic flux lines are continuous and closed.
Direction is that of the B vector at any point.
Flux lines are NOT in direction of force but ^.
When area A is perpendicular to flux:
The unit of flux density is the Weber per square meter.

9. Origin of Magnetic Fields
Recall that the strength of an electric field E was defined as the electric force per unit charge.
Since no isolated magnetic pole has ever been found, we can’t define the magnetic field B in terms of the magnetic force per unit north pole. + E
We will see instead that magnetic fields result from charges in motion—not from stationary charge or poles. This fact will be covered later. +
B v v ^

10. Magnetic Force on Moving Charge
Imagine a tube that projects charge +q with velocity v into perpendicular B field. N S B v F
Experiment shows:
Upward magnetic force F on charge moving in B field.
Each of the following results in a greater magnetic force F: an increase in velocity v, an increase in charge q, and a larger magnetic field B.

11. Direction of Magnetic Force
The right hand rule:
With a flat right hand, point thumb in direction of velocity v, fingers in direction of B field. The flat hand pushes in the direction of force F. B v F B v F N S
The force is greatest when the velocity v is perpendicular to the B field. The deflection decreases to zero for parallel motion.

12. Forces on Negative Charges
Forces on negative charges are opposite to those on positive charges. The force on the negative charge requires a reversal to show downward force F. N S N S F B v
Reversed rule for negative q B v F
Right-hand rule for positive q

13. Indicating Direction of B-fields
One way of indicating the directions of fields perpen-dicular to a plane is to use crosses X and dots · :
A field directed into the paper is denoted by a cross “X” like the tail feathers of an arrow.
X X X X X X X X X X X X X X X X
· · · ·
A field directed out of the paper is denoted by a dot “ ” like the front tip end of an arrow.

14. Practice With Directions:
What is the direction of the force F on the charge in each of the examples described below? Up F + 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 X X v +
Left F
· · · · Up F
· · · · - v - v F
Right
negative q

15. Zero deflection when FB = FE
Crossed E and B Fields
The motion of charged particles, such as electrons, can be controlled by combined electric and magnetic fields.
Note: FE on electron is upward and opposite E-field.
x x x x x x x x + - e- v
But, FB on electron is down (left-hand rule). B v FB - B v FE E e- -
Zero deflection when FB = FE

16. The Velocity Selector -
This device uses crossed fields to select only those velocities for which FB = FE. (Verify directions for +q)
When FB = FE :
x x x x x x x x + - +q v
Source of +q
Velocity selector
By adjusting the E and/or B-fields, a person can select only those ions with the desired velocity.

17. Example 2. A lithium ion, q = +1
Example 2. A lithium ion, q = +1.6 x C, is projected through a velocity selector where B = 20 mT. The E-field is adjusted to select a velocity of 1.5 x 106 m/s. What is the electric field E?
x x x x x x x x + - +q v
Source of +q V
E = vB
E = 3.00 x 104 V/m
E = (1.5 x 106 m/s)(20 x 10-3 T);

18. Circular Motion in B-field
The magnetic force F on a moving charge is always perpendicular to its velocity v. Thus, a charge moving in a B-field will experience a centripetal force.
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
Centripetal Fc = FB + R Fc
The radius of path is:

19. 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
Mass Spectrometer +q R + -
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
Photographic plate m1 m2
slit
Ions passed through a velocity selector at known velocity emerge into a magnetic field as shown. The radius is:
The mass is found by measuring the radius R:

20. 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
Example 3. A Neon ion, q = 1.6 x C, follows a path of radius 7.28 cm. Upper and lower B = 0.5 T and E = 1000 V/m. What is its mass? +q R + -
x x x x x x x x
Photographic plate m
slit
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
v = 2000 m/s
m = 2.91 x kg

21. Summary
The direction of forces on a charge moving in an electric field can be determined by the right-hand rule for positive charges and by the reversed rule for negative charges. N S B v F
Right-hand rule for positive q N S F B v
Reversed rule for negative q

22. Summary (Continued) F B v q v sin q
For a charge moving in a B-field, the magnitude of the force is given by:
F = qvB sin q

23. Summary (Continued) The velocity selector: - The mass spectrometer: -
x x x x x x x x + - +q v V +q R + -
x x x x x x x x m
slit
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
The mass spectrometer:

24. CONCLUSION: Chapter 29 Magnetic Fields