Sources of Magnetic Field Chapter 28 Sources of Magnetic Field

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

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.

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.

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.

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.

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

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

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.

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.

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.

Magnetic fields in coils Consider Figures 28.13, 28.14, and 28.15 below. Follow Example 28.6.

Ampere’s Law I—specific then general

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

Field inside a long cylindrical conductor A cylinder of radius R carrying a current I. Refer to Example 28.8 and Figure 28.20 and Figure 28.21.

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

Field of a toroidal solenoid A doughnut-shaped solenoid. Refer to Example 28.10 and Figure 28.25.

Magnetic materials The Bohr magneton will determine how to classify material. Refer to Figure 28.26 below. Follow Example 28.11. 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.

Magnetic materials II Consider Figure 28.27 at right. Consider Figure 28.28 below.

Magnetic materials III Consider Figure 28.29 below. Follow Example 28.12.