Conductors

A conductor is a special type of material which allows electrons to move freely. This means that electricity can easily flow through them. Most metals make great conductors such as copper, aluminum, and iron. There are several electrostatic properties of all conductors.

Let's explore each of these properties in more detail.

"The net E-field inside of a conductor is always zero."

When a conductor is placed in an E-field, the net E-field inside of that conductor is always zero. This is because when the conductor is placed in an E-field, the positive charges are going to be pushed to the surface furthest from the source of the E-field, while the electrons are going to be pulled to the surface closest to the source of the E-field. When this happens, the conductor becomes polarized. These polarized charges then create an equal and opposite E-field inside of the conductor which thus cancels out the original E-field.

"Any net charge of a conductor accumulates on its surface. "

Recall that one of the main defining characteristics of a conductor is that it enables charge to move freely inside of it. Consider a simple example for understanding. If a conductor has some positive charge Q, the protons inside of the conductor will repel each other and will want to be as far apart from each other as possible. The only way to achieve this is to reside on the surface of the conductor.

"The entire conductor is in equipotential."

Potential differences cause charges to move. If there were potential differences within a conductor, because charges are allowed to move freely, they would simply move until the conductor was in equipotential.

"The E-field produced by a conductor is always perpendicular to the surface of the conductor."

The simplest way to explain why the E-field is always perpendicular to the surface of the conductor is this: Any components of the E-field parallel to the surface will cause a movement of charges, rearranging the charges in such a way that breaks the first and third properties of conductors. Perpendicular E-field components, however, will not cause the movement of charge because the charges have nowhere to go since they are bounded by the surface or the repulsive force from the opposite side.

Capacitors

A capacitor is an electrical component used to store charge and consists of two conductors held a fixed distance away from eachother. The most common form of a capacitor is one made of two parallel plates.

When a capacitor stands alone, it is nothing more than two conductors considered together as a system - before current runs through a capacitor thus giving it charge, the capacitor acts as a wire. This fact will be incredibly useful during circuit analysis later on. However, as soon as a capacitor is hooked up to a battery (the positive end of the battery wired to one plate and the negative end wired to other), charge is forced onto one of the plates. This gives the first plate a positive charge. The positive charge on this first plate then repels the positive charge out of the second plate, leaving it with a negative charge of equal magnitude.

Once current has run through the capacitor for an appropriate amount of time, the capcaitor becomes fully charged. Both plates will have an equal and opposite charge, and no more charge can be forced through the capacitor. When a capacitor is fully charged, it acts like a broken wire. Again, this will be useful for circuit analysis later.

In the above figure, the capacitor is fully charged and no more current runs through it. There is a potential difference between the two plates as well as an E-field which is how energy is stored. Once a capictor is fully charged, it itself can now act as a temporary battery. If the voltage source (initial battery) is removed from the capacitor, a fixed potential difference is no longer being held across the plates. Instead, the charge will begin to flow until the capacitor runs out of charge and reverts to its original state.

The space between the two plates in a capacitor is technically air. However, it does not have to be. This space can also be filled by a material known as a dielectric. A dielectric is just another word for an insulator - the electrons cannot physically flow from plate to plate through the dielectric. All dielectrics have a dielectric constant, Κ.The dielectric constant of a material is a measure of how much energy it is capable of storing.

The capacitance, C, can be determined by

where ε is the permitivity of free space and is a constant. The unit of capacitance is the Farad, F. When the dielectric is air, Κ=1 and the capacitance becomes

These are some other equations that pertain to capacitors:

If capacitors are placed in parallel within a circuit, the total capacitance of the circuit is simply the sum of the individual capacitances.

However, capacitors placed in series will have a total capacitance of