5.6.2: Explorations

Exploration 1: Map Field Lines and Determine Forces

In the animation there is an object underneath the gray circle that creates a magnetic field. Restart.

1. Use the compass to determine the direction of the magnetic field. Sketch the vector field and the field lines for each configuration.
2. Check your field-line diagrams by double-clicking on the animation to show a field line at the location of the mouse.

Add a wire with current coming out of the screen (electrons moving into the screen). Click-drag the wire to move it around. The arrow shows the direction of the force on the wire.

3. Explain why the force vector points the way it does at two different locations of the wire for each configuration.
4. If the current was in the other direction, what direction would the force be at the two locations you chose? Explain.
5. Check your answer by adding a wire with current going into the screen.

Exploration authored by Anne J. Cox.

Exploration 2: Velocity Selector

A mass spectrometer measures the mass of particles. The first step in the operation of the mass spectrometer is to select particles of a particular velocity. As you work through this exploration you will see how a velocity selector operates. The animation shows a positively charged particle entering a constant magnetic field directed into the screen. Restart.

1. BEFORE you play the animation, PREDICT the path the charge will follow. I have already made my prediction; let me see the path. Were you correct? If not, what caused your error?

Now, suppose a constant electric field is added to the region with the magnetic field.

2. In which direction (right, left, up, down, into screen, or out of screen) should the electric field be oriented such that it could possibly cancel the force due to the magnetic field?
3. In order to create the electric field, two charged plates are used. Which plate should be positively charged and which should be negatively charged to create the desired field?
4. I have made a prediction; let me check my thinking. Were you correct? If not, what misunderstanding caused your error?
5. Derive a mathematical relationship between the electric field, the magnetic field, and the velocity a particle must have to pass through the region undeflected.
6. In the animation the electric field produced by the plates is \(600\text{ N/C}\) and the magnetic field is \(0.3\text{ T}\). Use your mathematical relationship to find the velocity the particles have in order to pass straight through the two fields. Once you have calculated your answer, put it in the box and press "play" to see if you were correct.

Exploration authored by Melissa Dancy and Wolfgang Christian.

Exploration 3: Mass Spectrometer

A negatively charged particle enters a region with a constant magnetic field directed into the screen and a constant electric field produced by two charged plates. If the particle is able to pass through the first region, it enters a region where only the magnetic field is present. Restart.

The Exploration demonstrates how a mass spectrometer works (See Illustration 23.4 and Exploration 25.4 for related examples). Many particles might be injected into the first region. For certain values of electric and magnetic fields, only particles with a particular velocity will pass through undeflected. By subjecting the particles to the velocity selector, we know the velocity of the particle when it enters the second region.

1. If the initial velocity is \(50\text{ m/s}\), the magnetic field is \(0.5\text{ T}\), the mass is \(0.3\) gram, and the charge is \(-1\times 10^{-3}\) coulombs, what must the electric field be in order to "select" the \(50\text{ m/s}\) particle? Calculate your answer first and then test it using the animation.
2. If you change the value of the magnetic field, is the \(50\text{ m/s}\) particle still "selected"?
3. What if you change the mass or the charge? Explain.
4. Once you are able to select the \(50\text{ m/s}\) particle and it passes into a region where only the magnetic field is present, it follows a circular path. Why?

Now change the mass from \(0.3\) gram to \(0.1\) gram. Notice that the curved path of the charge changes. For every mass, the curved path will be slightly different. This allows you to measure the mass of an individual particle. This is very useful, especially when the mass is too small to easily measure using other methods.

5. By considering the magnetic force in the second region, develop a mathematical expression that relates the mass of the particle to the other variables. Do not include the velocity in your expression. You can use the condition that the particle passed through the region of electric and magnetic fields undeflected to eliminate velocity from your expression. Your expression will also contain the radius of the circular path.

You can measure this radius in the applet using a mouse-down (position is given in meters and time is given in seconds). In a real mass spectrometer the radius is often measured by putting a photographic plate on the wall where the particle hits. When the particle hits the plate it leaves a mark, allowing the experimenter to determine the value of the radius.

6. Check the expression you derived. When you put in the values from above, do you get a mass of \(0.1\) gram as you should?

Exploration authored by Melissa Dancy.

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