### Unit 4: Magnetism

Earlier, we studied electric charges, potentials, and fields. We will now take a look at an important effect of moving charges: magnetism. Thales of Miletus set the stage for the scientific exploration of magnetism back in Ancient Greek times, when magnetism could only be observed via the behavior of natural magnets, called lodestones. Hans Christian Oersted first noted the relationship between moving electric charges and magnetism much later, when he accidentally discovered that an electric current could deflect a nearby compass needle in 1820. Forty-five years after Oersted made this observation, James Clerk Maxwell united electrical and magnetic phenomena into four reasonably simple equations known since as Maxwell's Equations.

**Completing this unit should take you approximately 7 hours.**

Upon successful completion of this unit, you will be able to:

- describe the magnetic field associated with a moving charge, a magnetic dipole, a long, straight current-carrying wire, a wire loop, and a solenoid;
- find the force exerted by a magnetic field on a moving charged particle;
- explain the fundamental difference between a magnetic and a non-magnetic material;
- state Ampere's law;
- solve problems involving the motion of a charged particle in a magnetic field; and
- solve problems using Ampere's law.

### 4.1: Magnetic Field

Read sections 22.1, 22.2, and 22.3. Think about the corresponding conceptual questions on the to assess your understanding of the sections.

This demonstration is designed to remind you of one of the most common elementary school demonstrations of magnetism, where fine iron filings decorate the lines of magnetic force, showing, as in the demonstration, the dipole-like magnetic field of a permanent magnet. If we place a ferromagnetic material, such as iron, in a magnetic field, it will induce a magnetic field in the iron that opposes the external field. As usual, one of Nature's rules is to arrange matters so that the total energy of the system is as small as possible. In this case, inducing an opposing field in the iron reduces the total magnetic energy. Because iron filings tend to be long and skinny, the induced field turns them into tiny bar magnets, with north and south poles aligned such that the north pole of the iron filing points along the local direction of the magnetic field and orients away from the north pole of the external magnet. Accordingly, when you place a few hundred iron filings on a surface over a magnet, you are able to visualize the magnetic lines of force.

### 4.2: Magnetic Force on Moving Electric Charges

Please watch this lecture series, pausing to take notes, before moving on to the reading below. Notice that since the force on a charge in a magnetic field is related to the cross-product of the charge's velocity and the field vector, two of the lectures are devoted to the review of the definition and calculation of the cross-product of two vectors.

Please click on the link above, select the links to the following subsections, and read these webpages in their entirety: "The Lorentz Force," "Charged Particle in a Magnetic Field," and "The Hall Effect." In addition, select the links for Examples 8.1 and 8.2, and work through these examples before looking at the solutions in the text. Make sure you understand not only the solutions but also how to approach solving the problem so that you can obtain the solution yourself. You will be responsible for being able to solve problems of this type on the final exam.

This is an idealized version of a classic laboratory experiment carried out with a cathode-ray tube. In this demonstration, you can see the entire path of the moving charge, rather than just its position at a screen (as you would with a cathode-ray tube). The initial velocity and magnetic field vectors are indicated, allowing you to determine the direction and strength of the Lorentz force on the moving charge. This demonstration does not provide any measurements of the trajectory of the charge, but you can observe how it changes qualitatively with the change of the parameters. As usual, change each parameter in turn while keeping the others constant, in order to make conclusions. What affects the radius of the spiral path? Compare your observation with the theoretical results in the reading resources. How does the angle between the magnetic field vector and initial velocity affect the shape of the spiral? What happens if their direction is the same, and how can this be explain using the Lorenz's force formula?

This demonstration shows the motion of an electric charge in uniform electric and magnetic fields. The charge, E field, and B field magnitudes are all controllable, as are the field orientations and the initial velocity vector of the charge. Note that for nearly all combinations of parameters, the result is that the charge spirals toward a position, comes to a stop save for circular motion, and then reflects back in roughly the original direction. Why?

### 4.3: Magnetic Field of a Current-Carrying Wire

Please watch this lecture series, pausing to take notes, before moving on to the reading below.

Read these sections: "Ampere Experiments", "Ampere's Law", "Ampère's Circuital Law," "Magnetic Field of a Solenoid," and "Gauss' Law for Magnetic Fields." In addition, click on the link to Example 8.3, and work through this example before looking at the solution. Make sure you understand not only the solution but also how to approach solving the problem so that you can obtain the solution yourself. You will be responsible for being able to solve problems of this type on the final exam.

This is a simulation of another classic classroom demonstration, in which you trace out the magnetic lines of force surrounding a current-carrying wire. The lines of magnetic force are circles surrounding the wire, and the direction of the magnetic field reverses when the current reverses. Practice using the right-hand rule to determine the direction of the magnetic field, and make sure you get the same result as in the demonstration.

This demonstration illustrates the magnetic field surrounding a current loop. The magnetic field has a cylindrical axis of symmetry on the axis of the current loop.

### 4.4: Magnetic Materials

Please read this section: "Origin of Permanent Magnetism."

This demonstration illustrates the process of magnetization of a magnetic material in an external field. As the magnetic domains (small bar magnets) become more highly aligned, the magnetic field produced by the material increases. Note that when all (or most) domains are aligned, the material cannot become more highly magnetized. This is the phenomenon of magnetic saturation.

### Unit 4 Assessment

Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

- This assessment