Instructions

This page is designed to get you started using the applet. The applet should be open. The step-by-step instructions on this page are to be done in the applet. You may need to toggle back and forth between instructions and applet if your screen space is limited.

Setting the Parameters That Determine the Particle's Orbit

Observing the Motion

Data

Zoom Slider

The motion of a particle in a magnetic field depends on the magnetic field , the initial velocity (0) of the particle, and the charge q and mass m of the particle. It will now be explained how you can vary these parameters and this way vary the particle's motion.

All parameter values are entered in SI-units. The units are not specified in the entry fields. For more comments on units, please see the section Data below.

1. Reset the applet. The magenta velocity vector should be visible. You can hide or display it by means of the Velocity toggle button . For the time being, keep it displayed.
2. Initial Position and Velocity. If the magnetic field is uniform, as it is in the applet, the initial position has no influence on the particle's motion, other than where the motion will occur. Therefore, and in order to make best use of the available space when displaying the orbits, the applet does not let you vary the particle's initial position. The particle will always start out at the center of the applet window.

   Important for the nature of the motion is the direction of the initial velocity relative to the direction of the magnetic field. In the applet the initial velocity is fixed to be horizontal and to the right, i.e., in the positive x-direction, but the direction of the magnetic field can be varied to some extent. It is not necessary to vary the directions of both the velocity and the field to be able to observe the range of possible motions.

3. Initial Speed. Set the initial speed v to 150 m/s with the Speed slider .

   Note that the speed cannot be adjusted by dragging the tip of the velocity vector.

4. Mass. Set the mass of the particle to 1.0 kg with the Mass slider .
5. Charge. Set the charge of the particle to 2.0 C with the Charge slider .
6. Magnetic Field. Set the magnitude B of the magnetic field to 2.0 T with the Magnetic-Field slider .

   Set the direction of the magnetic field to out-of-screen with the Magnetic Field Direction toggle button .

   You should obtain the display shown in Figure 1 below. The small circles indicate that the magnetic field is pointing towards the viewer. Think of the little circles as tips of arrows pointing towards you. To display the orbit (shown in blue in Figure 1), click Play and the Trace toggle button .

   

Figure 1

1. With the settings made above, click Play . Display the particle's track by selecting the Trace toggle button . You should be able to observe the particle moving along a circular path curving to the right, like that shown in Figure 1.
2. Click Rewind , and reverse the charge to -2.0 C without changing any of the other settings. Then click Play again. You should be able to observe a circular orbit exactly like that in Figure 1, but this time curving to the left.
3. Click Rewind, change the charge back to +2.0 C, but this time set the magnetic field direction to "into screen" by clicking the Magnetic Field Direction toggle button once. Little "x's" throughout the applet window indicate the field direction. You can think of the "x's" as tail ends of arrows viewed from behind.

   If you don't change any of the other settings, the motion should be just like the previous one, the same size circle as in Figure 1 but curving to the left.

4. Click Rewind once more, change the charge again to -2.0 C, but make no other changes. The magnetic field direction is still into the screen. The motion should be exactly as in Figure 1.
5. Finally, click Rewind and click the Magnetic Field direction button again so that it reads "to the right". Throughout the applet window little arrows pointing right indicate that the magnetic field is to the right everywhere. When you play the motion, you should be able to observe a constant-velocity motion to the right.
6. You can step through any motion by clicking the Step button . The step size cannot be varied.



Data

Set the applet to the settings made initially:

• m: 1.0 kg
• v: 150 m/s
• q: 2.0 C
• : magnitude 2.0 T, direction out of screen

In the Data Box in the top right corner of the applet, observe the values of the radius r of the circular orbit and the period T with which the particle moves through the circle. The Data Box is shown in Figure 2 below.



Figure 2

The radius and period are displayed without units, as are the slider values. The value of the radius r is in SI-units. However, the value of the period is not. To obtain the value of the period in seconds, muliply the value given in the Data Box by 2π.



Zoom Slider

Click Reset, and make the following settings in the applet:

• m: 3.0 kg
• v: 150 m/s
• q:1.0 C
• : magnitude 1.0 T, direction out of screen

Play the motion. You should find that the particle's orbit goes way off screen. If you wait long enough, the particle will return to its starting point.

To be able to see the entire orbit (most of it, anyway), as in Figure 3 below, click Rewind and set the Zoom slider to 1/6X.



Figure 3

The Zoom may have to be set to a different value, depending on the size of your window.



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