Shells and Conductors

What is a conductor?   Conductors are materials, for example, metals, through which charged particles move readily.   What is meant by the term "under electrostatic conditions?" Under electrostatic conditions, field lines must terminate or begin on the surface of a conductor - that is, there is no electric field within a conductor. If any field line penetrated into the conductor, then electrons would respond to its presence and be accelerated within the conductor. If that happened, the conductor would no longer be under electrostatic conditions. Under electrostatic conditions, field lines must meet the surface of a conductor at right angles. If any field line did NOT come it at a 90º angle, then a component of the field line would be parallel to the conductor’s surface and electrons would respond to its presence and be accelerated within the conductor. If that happened, the conductor would no longer be under electrostatic conditions. When a conductor is under electrostatic conditions, all charges (electrons) must be at rest. Don't forget that one coulomb of charge represents 6.25 x 1018 electrons.   Under electrostatic conditions, the entire conductor must be at the same potential, or voltage. If not, then charges would flow from points of high potential to points of lower potential. If that happened, the conductor would no longer be under electrostatic conditions.   Faraday's Ice-Pail Experiment Faraday started with a neutral metal ice pail (metal bucket) and an uncharged electroscope. He then suspended a positively charged metal ball into the ice pail, being careful to not touch the sides of the pail. The leaves of the electroscope diverged. Moreover, their degree of divergence was independent of the metal ball's exact location. Only when the metal ball was completely withdrawn did the leaves collapse back to their original position. Faraday noticed that if the metal ball was allowed to contact the inside surface of the ice pail, the leaves of the electroscope remained diverged. Afterwards, when he completely removed the ball from the inside of the ice pail, the leaves remained diverged. However, the metal ball was no longer charged. Since the leaves of the electroscope that was attached to the OUTSIDE of the pail did not move when the ball touched the inside of the pail, he concluded that the inner surface had just enough charge to neutralize the ball.   Conclusions: Faraday’s Ice Pail Experiment pg 330-331, Principles of Physics, Frederick Beuche, McGraw-Hill Book Company, New York, New York. 1988. A charged metal object suspended inside a neutral metal container INDUCES an equal but opposite charge on the inside of the container. When the charged metal object is touched to the inside of the of the container, the induced charge exactly neutralizes the excess charge on the object. When a charged object is placed within a metal container, an equal charge of the same sign is FORCED to the outer surface of the container. All of the charge on any metal object resides on its outer surface if a conducting path is provided so that the charge can move there. Remember that charges will flow between two positions as long as there is a potential difference between those positions. When the voltage has been equalized, all charges will cease to flow. Faraday Cage   An important consequence of this experiment is that electric fields can be shielded - that is, the outside of a conductor acts as a FARADAY CAGE. A closed metal surface, no matter what it's shape, will block out any external electric field lines. And, as long as there are no electric charges residing inside the metal cavity, the electric field in the interior will be ZERO everywhere. This is why you are safe inside your car or on an airplane during a lightning storm.   Electrical shielding is easily accomplished by surrounding the surface that you wish to shield with a conducting surface. The free charges on the conducting surface will arrange themselves in such a way as to insure that the electric field within the conductor equals zero. This is the reason why electrical components come in metal boxes, to shield them from outside electrical activity.   This principle of electrical shielding is an important distinction between electric fields and gravitational fields. Electric fields can be shielded since there are two (2) types of electric charges. However, gravitational fields CANNOT be shielded - the effects of the gravitational attraction between two objects can be felt through any and all intervening matter.

Conducting Shells     Consider the charged conducting sphere shown above. Since there are eight field lines illustrated, let's assume that its charge is +8 µC. When viewed from infinity, this charged sphere would look like a point charge with an electric field that agrees with the graph for E vs r shown above.   However, consider that this charged sphere could instead be constructed of a NEUTRAL thin conducting shell with a hidden positive point charge located at its center, as shown below.     According to the results of Faraday's Ice Pail Experiment, the positive point charge INDUCES an equal but opposite charge on the inside of the shell AND an equal but similar charge on the outside of the shell. Note that the shell remains neutral - eight field lines terminate on the surface of its inner shell and eight field lines originate on the surface of its outer shell. Remember that there would be NO field lines between the "inner and outer" surfaces of the conducting shell. The only field lines would be between the inside point charge and the shell's inner surface and outside of the shell's outer surface. All field lines should be symmetric and meet any equipotential surfaces at right angles. When viewed from infinitely far away, this configuration would look exactly like the original 8 µC charged sphere! Given below is a diagram of the electric fields for this conducting shell.     For the remainder of this lesson we will work some examples using conducting shells. In each case, the conducting shell is aqua in color and the point charge placed in its center is yellow in color.