5.6.1: Illustrations

Illustration 1: Magnets and Compass Needles

This Illustration allows you to consider the magnetic field around a bar magnet. By default, the page will load with a magnet in the center of the animation. Use the compass to explore the magnetic field around a bar magnet by dragging the compass around the magnet. A compass utilizes a small permanent magnet; its arrow points toward the north pole of its magnet. Make a diagram showing the direction the compass needle points at various locations. Include enough points to establish a pattern. Restart.

Now that you have completed this diagram, turn the magnetic field vectors on to see this representation of the magnetic field. Does your diagram look like that of the animation's field vectors? It should. The magnetic field vectors are like little compass needles placed at various points around space. The color of the arrow of the magnetic field vector represents the strength of the field at the point, while the arrow shows the direction of the field.

You can also double click at any point in the animation to draw a magnetic field line through that point, which yields another representation. There will be a small delay after double clicking before the line appears (the line needs to be calculated). Double click at enough points to get an accurate picture of the magnetic field lines around the magnet. What is the difference between the field vectors and the field lines? Notice that in the field-line representation the field lines are tangent to the field vectors and also tangent to the direction of a compass needle placed at that point. In the field-line representation the field lines are drawn with the same color. In the field-vector representation the strength of the field is depicted in the color of the field vectors. How do we represent the magnitude of the magnetic field in the field-line representation? The density of field lines (lines per square length unit) is greater where the field is stronger.

Clear the screen. Place two magnets beside each other with the north pole of one lined up with the south pole of the other:

Figure \(\PageIndex{1}\)

Display the field vectors and/or double click to display the magnetic field lines. How does the magnetic field of the two magnets compare to the field of one magnet? What do your observations suggest about how a bar magnet would behave when broken in half? The magnetic field vectors and lines for the above configuration look just like those for one large magnet. In fact, if you broke a bar magnet in half, what you would get would be two bar magnets, each with their own north and south pole. This is because there are no magnetic monopoles in classical magnetism. There are electric monopoles, which we call electric charges.

Predict what the magnetic field will be if you place a north-south magnet directly on top of a south-north magnet. Try it.

Illustration authored by Melissa Dancy.
Script authored by Morten Brydensholt.

Illustration 2: Earth's Magnetic Field

This Illustration demonstrates the magnetic field of Earth. We describe the magnetic field by mapping out magnetic field vectors and/or magnetic field lines. This Illustration allows you to try both representations. What is the difference between the two representations? Restart.

Before adding either field vectors or field lines, add a compass and move it around. A compass utilizes a small permanent magnet; its arrow points toward the north pole of its magnet. Now show the field vectors. Notice that the compass arrow lines up with the field vectors. The field vectors essentially tell you where little compass needles would point at different places. Now show the field lines. On the field-line representation, notice that the compass needle is always tangent to the field line.

Now show the geographic poles of Earth. Move the compass around (again the compass is a little magnet with the arrow on its north pole). Is the geographic north pole also the magnetic north pole? Check your answer by showing the magnetic poles.

Why do you think we call the pole in the Arctic the North Pole? This is because the north pole of a compass points there (even though by this definition the North Pole is a south pole). Although we know where the poles are on Earth at the present time, over thousands of years the magnetic north and south poles have flipped back and forth, and we do not yet have a satisfactory theory that explains what causes Earth's magnetic field.

Illustration authored by Morten Brydensholt and modified by Anne J. Cox.

Illustration 3: A Mass Spectrometer

Begin this animation by selecting the Multiple Masses Demonstration. This shows five particles passing through a model of a mass spectrometer. The particles have different masses but are otherwise identical. Notice how the particles are separated based on their mass. Restart.

You can enter values for the initial conditions and then press the "register values and play" button to see a single particle pass through the mass spectrometer. The particle initially enters a region with an electric field directed downward and a magnetic field directed into the screen. Since the particle is negatively charged, the electric field exerts an upward force (\(\mathbf{F}=q\mathbf{E}\); see, for example, Illustration 23.4) and the magnetic field initially exerts a downward force (\(\mathbf{F}=q\mathbf{v}\times\mathbf{B}\)). Try setting the magnetic or the electric field to zero to see the effect of just one field on the particle. For certain values of the magnetic and electric fields, the magnetic and electric forces on the particle will exactly cancel and the particle will pass through the first region. This region is called a velocity selector, since only particles with a certain initial velocity will pass through for given values of the magnetic and electric fields. Other Explorations and Problems from this chapter will require you to formulate a mathematical relationship between the initial values for particles that pass through the velocity selector.

If a particle is able to pass through the first region, it enters a region where only the magnetic field is present. Since the magnetic field exerts a force perpendicular to the direction of the velocity (\(\mathbf{F}=q\mathbf{v}\times\mathbf{B}\)), the particle follows a circular path (since \(v\) and \(B\) are constant and \(\mathbf{v}\) and \(\mathbf{B}\) are perpendicular). The radius of this path depends on the mass. From Newton's second law for uniform circular motion, \(|\mathbf{F}| = mv^{2}/R = q|\mathbf{v}\times\mathbf{B}|= qvB\), since \(\mathbf{v}\) and \(\mathbf{B}\) are perpendicular. By measuring where the particle strikes one of the walls, you can determine the mass of the particle.

Illustration authored by Melissa Dancy and Wolfgang Christian.

Illustration 4: Magnetic Forces on Currents

This Illustration shows current flowing through a wire. A current consists of charges moving through a conducting wire (\(1\) coulomb of charge per second \(= 1\) ampere). This can occur in a conductor since charges in a conductor are free to move in response to forces. Restart.

In the animation there is initially no magnetic field in the region shown. The electrons (the charge carriers that are free to move in conductors) travel in one direction, but the direction of the current is in the opposite direction (it is the direction positive charges would flow). There is nothing strange about this; it is just a convention. A positive current in a particular direction means that it is as if positive charges are flowing in that direction (this is equivalent to negatively charged electrons flowing in the opposite direction). What is the direction of the current in this animation? As there are negative charges moving to the left, there is a positive current to the right.

Turn on the uniform magnetic field pointing into the screen. Notice that we represent the field by a series of circles with "\(x\)"s inside them. Since we represent vectors with arrows, the "\(x\)" is supposed to represent what it would look like if you saw an arrow moving away from you. You would see the back view of an arrow and the "\(x\)" made by the feathered-end of the arrow. Similarly, for a magnetic field pointing out of the page, we use a series of circles with dots inside them (the view of an arrow point coming right at you). From where the electrons are located, what direction is the force on the electrons? Switch the direction of the magnetic field (out of the page). Now what is the direction of the force on the electrons? Notice that the electrons are moving to the left. We can use \(\mathbf{F}=q\mathbf{v}\times\mathbf{B}\) to determine the force. For the uniform magnetic field pointing into the screen, \(q\) is negative, \(\mathbf{v}\) is to the right, and \(\mathbf{B}\) is out of the page. Since \(\mathbf{v}\) and \(\mathbf{B}\) are perpendicular, we have that \(F = |\mathbf{F}| = |q|vB\). The right-hand rule (point your fingers towards \(v\), curl them towards \(B\), the direction your thumb points is the direction of \(\mathbf{v}\times\mathbf{B}\)) gives downward for the force direction, but we must factor in the fact that we have negative charge. Thus, the force on the electrons in this case is upward. When we go through the same process for magnetic field (out of the page), we get that the force on the electrons is downward.

Change the direction the electrons are moving. Turn on the magnetic field into the page. What direction is the force now? If you followed the arguments of the previous paragraph, this should be easy.

With the electrons moving in the original direction, try a magnetic field pointing to the right. What is the direction of the force? What do you expect for a magnetic field pointing left? Try it. What can you conclude about the force on a moving charge (and, therefore, the force on a wire) in a magnetic field?

The force on a moving charged particle is perpendicular to both the velocity and the magnetic field (and the velocity and magnetic field cannot point in the same direction) and is described by the vector product or cross product \(F = q\mathbf{v}\times\mathbf{B}\). Remember that the charge on the electron is negative, so the force points in the opposite direction from \(\mathbf{v}\times\mathbf{B}\).

Illustration authored by Anne J. Cox.
Script authored by Morten Brydensholt and modified by Anne J. Cox.

Illustration 5: Permanent Magnets and Ferromagnetism

This is a simplified model of permanent magnets called the Ising model. In this Illustration you can change the temperature and background magnetic field to see how these variables affect the production of permanent magnets. Restart.

To turn an ordinary nail into a magnet, you can put it in a magnetic field. The iron will be magnetized and it will retain its magnetization even when the field is removed. This model illustrates how that is possible. The red and green represent regions within a material with magnetic moments that are lined up in one direction (red) and the other direction (green). After you push "play," notice that, to begin with, there are essentially equal areas of red and green regions. This is recorded on the graph as a magnetization of about \(0\). This means that inside our iron there is no organization of the magnetic moments. The thermal energy available in the material allows for the changing between red and green that you see.

Put this material in a magnetic field (push the "\(B > 0\)" button). What happens? Now the magnetic moments (little magnets inside the material) are lined up with the applied field. What do you expect will happen if you push the "\(B < 0\)" button? Why? Try it.

Now, what do you expect will happen if you push the "\(B = 0\)" button? Try that. What happens? Does the magnetization go to zero right away? Even when the magnetic field is no longer in place, the magnets want to stay lined up. It takes energy to disorganize them again. Over a long period of time, they can get randomly oriented again, but they will line back up quickly with an external field. Verify this.

Another way to get the magnets randomly oriented again is to increase the temperature (give them enough thermal energy to destroy the order). To simulate this, first magnetize the material (either red or green), set the field back to zero and then push the "increase temperature" button.

Illustration authored by Anne J. Cox.
Script authored by Wolfgang Christian and modified by Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.