Electric field patterns

This apparatus consists of several sets of electrodes in various configurations, a frame to hold them and allow connections to a high voltage supply, and an observation tank that contains a light silicone oil and fine, colored wood chips. The black-and-blue box at left in the photograph above is a power supply that provides a potential of about 7 kilovolts when you press the red button (a momentary-contact switch). The electrodes are mounted on transparent plastic sheets, and the faces of the observation tank are also transparent, so that when you place the apparatus on an overhead projector, you can project an image of the field pattern onto a screen for the whole class to see.

The set includes five electrode configurations: 1) A pair of parallel plates, 2) Two oppositely-charged posts, 3) Two like-charged posts surrounded by a rectangular ground electrode, 4) A post in the center of an ovoid outer electrode (which charge oppositely), and 5) A roughly circular electrode in the center of a larger ovoid electrode (which charge oppositely), to show Gauss’s law.

To use the apparatus, insert the desired electrode set into the holder, electrode side up, with the contacts toward the back. Set the contacts on the electrode set against the holder contacts, then push the other end of the plate forward and downward, pressing it until the electrode set is all the way into the holder. Now take the observation tank, and shake it (somewhat vigorously) to disperse the wood chips as evenly as possible. Then, holding it vertical, with the smaller chamber at the top, tilt it from side to side to let the air bubbles escape into the smaller chamber. With the fill port (the disc with the screw in it, at the top right corner) up, set the tank on top of the electrode set. Lower the front end (the end of the large chamber, towards you) first, to avoid having air bubbles escape the small chamber.) Switch the power supply on, if it is not already on, by pressing the black rocker switch. Press the red button. You (and the class) will see the wood chips that lie between the electrodes, move so that they become oriented along electric field lines, revealing their pattern. Because the wood chips tend to settle, it is best to allow as little time as possible to elapse between when you shake the tank and when you energize the electrodes after you have set the tank on them. The photographs below show the electric field patterns that you obtain with the various electrode sets. Clicking on each image opens a larger-size photograph. An explanation of the physics follows the photographs.


Parallel plates
Oppositely charged points
Similarly charged points
Single charged point
Gauss’s law

Parallel plates

Two oppositely charged points

Two similarly charged points

Single point in oppositely charged ovoid

Circle inside oppositely charged ovoid


Demonstrations 56.03 – Attract paper bits with charged rod, and 56.06 – Electrostatically charged rods, show the repulsive force that exists between like charges, and the attractive force that exists between unlike charges. The presence of such a force on an electrically charged object indicates the presence of an electric field. For example, if we take a charged rod and bring it near a second, similarly charged rod, it experiences a force due to the electric field set up by the second rod. The first rod also sets up an electric field, thereby exerting an equal and opposite force on the second rod as Newton’s third law indicates should happen. If we imagine placing a test charge having a charge q at some point in the field, E, produced by a charged object, the magnitude of the electric field at that point is defined as the force on the test charge divided by the amount of charge on it, or E = F/q. Its units are newtons/coulomb (N/C).

The shape of this field, that is, what its magnitude is at various points in the space around a charged object, depends on the shape of the object, the amount of charge on it, and the shapes of, and charges on, any other objects nearby. To help visualize electric (and magnetic) fields, Michael Faraday introduced the concept of lines of force. These are imaginary lines, which we draw such that the tangent of one at any point gives the direction of E there, and their density – the number of lines passing through unit cross-sectional area (perpendicular to the lines) – gives the magnitude of E. (The greater the density of lines, the greater the magnitude of E, and the fewer lines per unit area, the smaller the magnitude of E.) A line of force cannot begin or end in the space around a charge, but must begin at a charge and end at another of opposite sign. In the case of an isolated charge, we can think of the lines radiating from it as ending at many charges at great distance from the individual charge.

If we suspend small fibers in a fluid insulating medium, such as the wood chips in silicone oil in the apparatus shown above, and then place them in an electric field, the fibers become polarized and, if not aligned with the field lines, they suffer a torque that aligns them so. Hence the patterns shown above. For the parallel plates, we see parallel lines, perpendicular to the plates, spanning the gap between them (with some curved lines at the ends). For the oppositely charged points, we see curved lines connecting the two points. For the similarly charged points, we see lines radiating from each point, and those going toward the opposite point bend away from the center. For the single point in the oppositely charged ovoid, we see lines radiating uniformly outwards toward the ovoid. The pattern for the last set of electrodes – the circle inside the ovoid – is particularly interesting, and illustrates an important consequence of Gauss’s law for electricity, which is that the electric field within a closed conductor is zero. Thus, we see a pattern of straight lines between the inner and outer conductor, but no pattern within the circle.

References:

1) Sears, Francis Weston, and Zemansky, Mark W. College Physics, Third Edition (Reading, Massachusetts: 1960), pp. 467-81.
2) Halliday, David, and Resnick, Robert Physics, Part Two, Third Edition. (New York: John Wiley and Sons: 1978), pp. 580-5, 601-11.