1. Sources of Magnetic Field
Chapter 28
Sources of Magnetic Field

2. Goals for Chapter 28
To study the magnetic field generated by a moving charge
To consider magnetic field of a current-carrying conductor
To examine the magnetic field of a long, straight, current-carrying conductor
To study the magnetic force between current-carrying conductors
To consider the magnetic field of a current loop
To examine and use Ampere’s Law

3. Introduction
Normally, when someone describes a solenoid, they are likely to use a doorbell or car-starter as their example. In the photo at right, scientists at CERN are using the most powerful magnetic field ever proposed.

4. The magnetic field of a moving charge
A moving charge will generate a magnetic field relative to the velocity of the charge.
See Figure 28.1 at right.

5. Moving charges—field lines
The moving charge will generate field lines in circles around the charge in planes perpendicular to the line of motion.
Follow Example 28.1.
Refer to Figure 28.2.

6. Magnetic field of a current element
The magnetic field of several moving charges will be the vector sum of each field.
Refer to Figure 28.3 at right.
Consider Problem-Solving Strategy 28.1.

7. Magnetic field of a current element II
Follow Example 28.2 and Figure 28.4 below.

8. Magnetic field of a straight current-carrying conductor
Biot and Savart contributed to finding the magnetic field produced by a single current-carrying conductor.

9. Fields around single wires
Refer to Example 28.3.
Refer to Example 28.4.
Figure 28.7 illustrates Example 28.4.
These apply to wires like the one at right in Figure 28.8.

10. Forces and parallel conductors
This is a classic demonstration. When you run the current one way through one rod and the other way through the second, they will snap together. If you reverse the connections on one rod so that both currents run the same way, the rods will fly apart.
Follow Example 28.5.
Figure 28.9 illustrates this concept.

11. Magnetic field of a circular current loop
A loop in the x,y plane will experience magnetic attraction or repulsion above and below the loop.

12. Magnetic fields in coils
Consider Figures 28.13, 28.14, and below.
Follow Example 28.6.

13. Ampere’s Law I—specific then general

14. Ampere’s Law II Consider Figure 28.18.
Follow Problem-Solving Strategy 28.2.
Follow Example 28.7.

15. Field inside a long cylindrical conductor
A cylinder of radius R carrying a current I.
Refer to Example 28.8 and Figure and Figure

16. Field of a solenoid A helical winding of wire on a cylinder.
Refer to Example 28.9 and Figures 28.22–28.24.

17. Field of a toroidal solenoid
A doughnut-shaped solenoid.
Refer to Example and Figure

18. Magnetic materials
The Bohr magneton will determine how to classify material. Refer to Figure below. Follow Example
Ferromagnetic, paramagnetic, and diamagnetic will help us designate material that’s naturally magnetized or magnetizable, material that can be influenced by a magnetic field, and finally, material that is not interactive with a magnetic field. Table 28.1 at right will aid any calculation.

19. Magnetic materials II Consider Figure 28.27 at right.
Consider Figure below.

20. Magnetic materials III
Consider Figure below.
Follow Example