## Illustration 22.2: Charge and Mass

This Illustration shows a fixed charge at the center and one or more test charges (depending on whether you choose Animation 1 or Animation 2) that move under the influence of the fixed charge. Run the animations and observe the motion of the test charges. You can reset the animations and click-drag the test charges. Can you determine the sign of the fixed charge? In other words, is the fixed charge positive or negative? Can you determine the mass of the test charge? What can you say about the force between the fixed charge and the test charge? How is the interaction similar to and how is it different from Newton's universal law of gravitation? These questions are of fundamental importance to physicists who must try to determine the charge, mass, and other physical properties of elementary particles using trajectories produced in experiments at high-energy particle accelerator laboratories throughout the world. Restart.

A test charge is defined as a positively charged object whose charge is so small that it does not influence other objects, including other test charges. Therefore, in these animations we assume that the fixed object has much more charge than the test charge(s) so that the motion of the test charges is determined by the Coulomb interaction with the fixed charge. This is similar to having a number of satellites in orbit around Earth. We usually ignore the gravitational attraction between satellites and only consider a satellite's attraction to Earth, and maybe the moon and Sun, when we calculate the satellite's trajectory. In Animation 2 what are the directions of the forces on the red and green test charges? The directions are radially outward just as it is for only one test charge in Animation 1. Remember, we are ignoring the effect of the test charges on each other's motions.

In Animation 2, if the test charges have the same mass, can you determine which test charge, red or green, has the bigger charge? If the mass is the same, comparing the accelerations will tell you about the force and, therefore, the charge on the test charge. What if the test objects had different masses as well as different charges? Would this change your answer? The ratio of charge to mass is now proportional to the acceleration, and this ratio affects the motion that you observe. In general, it is not easy to untangle the combination of charge and mass on the motion of charged particles. Early experiments using particle trajectories were performed in 1887 by Joseph J. Thompson and led to the realization that electrons are charged particles, but it took another 24 years before Robert A. Millikan was able to separate the effect of charge from that of mass.

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

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