Chapter 28 Magnetism

Magnetism is the set of phenomena that result due to the effects of Special Relativity on moving charges.

Some rocks have a slight magnetic effect. These rocks were known to the Greeks (near the city of Magnesia). Magnetic ores were studied in China before 300 A.D. The magnetic effects caused by current in a wire was discovered in 1821. The basic equations that connect electricity and magnetism were developed around 1860.

page 2 Two Garden Peas

You should review this material that reinforces the early discussion in the text that the electrical force is much, much larger than the gravitational force when there is a net charge on the objects.

page 4 A Thought (Gedanken) Experiment

Lorentz Contraction: Moving objects are shorter in the direction parallel to their velocity. What questions do you have on pages 4 and 5, especially Figure 2b?

page 6 Charge Density

We will skip these calculations.

page 7 A Proposed Experiment

We will skip the calculations and concentrate on the concepts.

page 8 Origin of Magnetic Forces

You should read this section before you view the movie on the CDROM that came with the textbook. One frame from the short movie is shown in Figure 6d. The force is real. It is called the magnetic force.

page 10 Magnetic Forces

The electric and magnetic forces are related.

Magnetic Force Law

For a long straight wire carrying current, I, the magnetic force on a moving charged particle is

F = q (velocity)[I/(2 pi r epsilon c squared) ]

The magnetic field strength is given by the factor inside the square brackets.

F = q v B In this calculation the velocity and magnetic field vectors are perpendicular to each other.

page 11 Direction of the Magnetic Field

page 12 Figures 10b and 11 show that the magnetic field is a circle around a wire that is carrying current.

page 13 Figure 12 has a bar magnet (rectangle) under a piece of cardboard. Iron filings are sprinkled on top of the cardboard to show the presence of the magnetic field.

The Right Hand Rule for Currents

* In determining the direction of the magnetic field due to the current in a wire, what direction do you point the thumb of your right hand?

What questions do you have on Figure 14?

page 14 Parallel Currents Attract

When two long straight wires are parallel to each other with currents in the same direction the wires experience a force that tends to pull them closer to each other. When two long straight wires are parallel to each other with currents in opposite directions the wires experience a force that tends to push them apart. This will be developed in the next section.

The Magnetic Force Law

F = qvB This calculation gives the maximum value for the magnetic force. It is observed that if the direction of the velocity is parallel to the direction of the magnetic field the magnetic force is zero. The maximum force exists when the direction of the velocity is perpendicular to the direction of the magnetic field.

For intermediate angles, F = qvB sin(theta), where theta is the angle between the velocity direction and the magnetic field direction.

page 15 Lorentz Force Law

F = qE + qvB gives the foce due to the electric and magnetic field on a charged particle. What are some differences in the terms qE and qvB?

page 16 Dimensions (Units) of the Magnetic FIeld, Tesla and Gauss

The standard metric unit for the strength of the magnetic field is the Tesla. This is a large unit. In more common situations the gauss is a convenient unit. 1 gauss = 10^-4 Tesla

Uniform Magnetic Fields

In what situations did we work with an Electric field that was constant (uniform) over a region of space?

A uniform B field has a constant value for the magnitude and direction of B in a region of space. Figures 18, 20 and 21a show approximately uniform B fields. Figure 18 shows a permanent magnet. There is no external electrical current (supplied by a battery or power supply) in this magnet. This is not a picture of an electromagnet. I will give one bonus point to the first person who sends me e-mail with the correct explanation as to why a permanent magnet possesses a magnetic field.

Why are the calculations for the magnetic force easier to perform when the B field is uniform?

Explain why the B field inside a solenoid is approximately uniform. In drawings of B field, like E field, when the lines are further apart the field is weaker.

page 18 Helmholtz Coils

We will skip this section

page 19 Motion of Charged Particles in Magnetic Fields

F = q v B sin (theta) The direction of the force is given by the Right-Hand-Rule. The direction of the force is ALWAYS perpendicular to the direction of the velocity AND the direction of the magnetic field. From our first semester of physics you may recall that Work = F d cos(theta). There is no work done if the force is perpendicular to the displacement.

*Calculate the work done on a 2 microCoulomb charge that is moving at 55 m/s in a 0.03 Tesla magnetic field if the velocity is perpendicular to the magnetic field.

The magnetic force does change the direction of the velocity of a moving charged particle.

page 20 Motion in a Uniform Magnetic Field

What type of motion does a positively charged particle have in a uniform B field?

What type of motion does a negatively charged particle have in a uniform B field?

What is different about the motions if the particles were shot into the B field from the same point at the same velocity?

Suppose a magnetic field is horizontal in this classroom with a strength of 2 x 10^-5 Teslas to the North. Describe the path of an electron initially moving upward in the classroom at 30,000 m/s. (Ignore collisions with the air molecules.)

qvB = mv² /r

page 22 Particle Accelerators (i.e. atom smashers !)

*How is the velocity of the electrons increased in a synchrotron?

Why is the strength of the magnetic field increased as the electrons’ velocity increases?

Figure 29 shows the top of the proton accelerator ring at Fermi Lab. Calculate the diameter of the ring.

page 24 Figure 30 shows the size of the Large Electron-Positron collider at CERN. Calculate its diameter.

Why are these large devices constructed rather than just doing this work on a synchrotron that fits in a lab room?

(Trivia: The World Wide Web concept (web pages, not the Internet) was developed at CERN.)

page 24 Relativistic Energy and Momenta

We will skip this section.

page 26 Bubble Chambers

We may come back to this section when we discuss nuclear physics.

page 28 The Mass Spectrometer

Spectrometers were developed in the late 1800’s to record the wavelengths of light (the spectrum). The mass spectrometer is a device that can be used to measure the mass of an atom. It was developed in the 1920’s.

Calculate the difference in positions on the photographic film in a mass spectrometer for C12 and C14 , ionized one time. Let the B field be 2 Gauss and the velocity be 3000 m/s for both ions.

What is a velocity selector?

page 29 Magnetic Focusing

We will skip this topic.

page 31 Space Physics

There are moving charged particles and magnetic fields in space.

page 31 The Magnetic Bottle

Verify that the magnetic force at the ends of the magnetic bottle is a restoring force.

page 32 Van Allen Radiation Belts

The dipole magnetic field of the earth is shown in Figure 42. Where is this field the strongest?

This field can trap charged particles. The concentration of the particles at certain distances from the earth form the radiation belts. Astronauts try to minimize the time exposure to the radiation in these belts.

The sun emits charged particles that encounter the earth. Where would you expect the particles to enter the earth’s atmosphere?

page 33 Auroras

When the charged particles hit molecules in the earth’s atmosphere those gas molecules become energized. The molecules can give up some of this extra energy by emitting light. The photographs of the aurora record the light given off by the molecules. The photographs are not showing directly the charged particles. You can view pictures of the aurora at these sites:

Miscellaneous Topics

How many "poles" does a magnet have?

What happens when a bar magnet is cut in half?

How does a traditional compass needle indicate the direction of the magnetic field?

Is the magnetic field of the earth similar in pattern to the magnetic field of a bar magnet?

How does the position of the earth’s north magnetic pole compare to the position of the north geographic pole?

Why is it unlikely that at large bar magnet in the interior of the earth is responsible for the earth’s magnetic field?

magnetic declination

dip angle

Have magnetic monopoles been detected?