What are dielectrics?
Dielectrics are materials that don’t allow current to flow. They are more often called insulators because they are the exact opposite of conductors. But usually when people call insulators “dielectrics,” it’s because they want to draw attention to a special property shared by all insulators: polarizability.
When a battery is connected to a conductor, the potential difference of the two poles of the battery pushes on all the charges in the conductor, which in turn causes them to drift slowly through the material—creating a current through the conductor. This happens because the outer electrons in a conductor are not attached to particular nuclei; they can wander freely throughout the entire material. In a dielectric, the charges are valence electrons that are stuck inside atoms of a crystal or polymer, and so current doesn’t flow at all. The electric field, however, still exerts a force on the charges. While the individual electrons remain tied to their parent atoms, they prefer to stay on the side of the atom that’s closer to the positive terminal. You can imagine the electrons wanting to jump off their parent atoms, but instead remaining leashed to them by the electrostatic forces that bind valence electrons to the nucleus:
Drawing showing the different ways electrons move in a dielectric versus a conductor,
In the drawing, the “leash” that ties the electrons to atoms has been drawn to look like a spring. Just like a spring, the force that causes electrons to orbit the nucleus provides a restoring force that counteracts the force exerted by the external electric field from the battery. So as the battery’s electric field pushes the electrons further and further towards one side of the atom, the restoring force in the opposite direction that pulls them back towards the nucleus gradually increases. The final position of the electrons corresponds to when these two forces (the one from the nucleus and the one from the battery) balance each other out.
Because the external field causes the electrons in each atom to congregate on one side of the nucleus, the atoms are polarized, meaning they have a positive pole and a negative pole that are oriented with the direction of the electric field.
That said, if a large enough electric field is applied to a dielectric, the forces that want to push the electrons can actually overcome the force that tethers them to the atomic nucleus, resulting in the electrons being ripped off their leashes. Large electric fields ionize the atoms of a dielectric. This means large electric fields create free charges (electrons in this case) that are able to move freely through the material and carry current. This process is called dielectric breakdown because the dielectric transitions from being an insulator to a conductor. In most real-world capacitors, dielectric breakdown results in a spark and damage to the capacitor.
How do dielectrics alter capacitors?
The presence of a dielectric in the gap of a parallel-plate capacitor increases the total capacitance. The equation that predicts this behavior looks like:
C = k C
C is the final capacitance (which is determined by the size and shape of the capacitor) and C is the capacitance without the dielectric. The dielectric constant, k, is a property of the specific dielectric being used; it indicates how much the capacitance increases when a given dielectric is used. The higher the dielectric constant, the better a material functions as an insulator---for example, rubber has a very high dielectric constant, and so it is often used a protective coating around high voltage wires because its high k makes it a very poor conductor.
Common dielectrics include wood (k = 2), beeswax (k = 4), glass (k = 5), and plastic (k = 5). The capacitors inside consumer electronics like your computer usually use plastic as a dielectric because of its low cost and high dielectric constant value, allowing the capacitors to be made really small.
The presence of a dielectric increases the capacitance because it actually decreases the electric field inside the capacitor by a factor of the dielectric constant. When all of the atoms in a dielectric polarize, they end up creating a field that points in the opposite direction to the applied field, resulting in a smaller field electric field:
Diagram showing the difference in voltage across a capacitor with a dielectric.
The presence of a dielectric between the two plates actually decreases the electric field inside the capacitor. This should tell you a lot about the way that sticking dielectrics in capacitors messes with their properties: capacitors store energy within their electric fields, and so changing that field changes everything!
For example, imagine that you’ve charged up your favorite parallel plate capacitor to a voltage of 6V across the plates. This 6V difference corresponds to an electric field between the plates, which is the voltage divided by the distance between the plates, d. If you have a huge capacitor with a plate separation of 1 cm, that’s an electric field of 6 V/cm. But imagine that you stick a big chunk of beeswax (k = 3) into your capacitor after it’s been fully charged and disconnected from the battery. All of the sudden, the charges on the molecules in the beeswax will shift and orient themselves in such a way that they partly cancel out the original field. Because the total amount of polarization is related to the dielectric constant, your capacitor now has an internal field of only 6/3 = 2 V/cm. Since the plate separation is the same, this corresponds to a new capacitor voltage of only 2V!
Drawing showing the change in voltage when a beeswax dielectric is added.
Another way to think about this is to remember that Q = CV, where Q is the charge of the capacitor, V is the voltage difference across the two plates, and C is the capacitance. For this setup, Q is fixed because the capacitor is not connected to any power source that can change the relative amount of charge on the two plates. Since adding the dielectric increases C by a factor of 3, the voltage must decrease by a factor of three in order to keep Q the same. You can now plug the new values of Q, C, V into the equation for the energy stored in a capacitor, E = 1/2 C V, and determine that the energy stored in the capacitor also decreases by a factor of 3.
The situation is very different when you leave the capacitor connected to the 6V battery as you insert the dielectric. This time the voltage, V, is fixed at 6V in the equation Q = CV, and so when you add the dielectric and cause the capacitance to jump by a factor of 3, the difference in charge across the two plates, Q, also increases by a factor of 3. In this situation, using the formula E = 1/2 C V reveals that the energy stored in the capacitor actually increases by a factor of three.
Consider the following… avoiding lightning strikes
If you’re ever in danger of being struck by lightning, sometimes all of the hairs on your head will stand on end until your head looks like a giant puff ball. This usually provides a good warning that you should immediately take shelter or move away from where you are and take cover indoors. It turns out that the reason for this odd effect is that your hair itself is a dielectric!
When you’re dealing with the kinds of voltages found in lightning strikes, the soggy ground beneath you is pretty conductive, and your body is, too. But your hair is not conductive. Human hair is such a good insulator that it actually used to be used as shielding in some old-school electrostatic machines. Thus if lightning is about to strike you, your hair acts like the dielectric in a capacitor, where the two conducting plates are the clouds (which have a huge negative charge) and the soggy ground below (which builds up a large positive charge due to induction). Thus, as charge builds up in the cloud, an electric field builds up in your hair. But unlike the glass or plastic inside a parallel-plate capacitor, the strands of your hair can easily move around individually, and so the electric field causes them to rise up, towards the clouds. Just like the individual electrons in a polarizable dielectric, the charges in them want to complete the circuit and travel up to the clouds, but they can’t quite make it because they are tethered to your head!
The electric fields that give rise to this effect look something like this:
When lightning eventually does strike, it serves as a sort of dielectric breakdown in which current can suddenly flow through the air and your hair, through your body, and into the ground---so be sure to make a run for it before that happens!
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