before the plates were pulled apart. Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and are separated by a distance d. Suppose the plates are pulled apart until they are separated by a distance D > d. The electrostatic energy stored in the capacitor is 1. greater than 2. the same as 3. smaller than before the plates were pulled apart. Q is constant and C decreases with increased separation distance Answer: 1. Since the oppositely charged plates are attracted to each other, work must be done to increase the separation between them. Thus, the electrostatic energy stored in the capacitor increases when the plates are separated. Work must be done on the plates to separate them since the plates are attracted to each other. If you do work on the system you are increasing the potential energy.

Dielectrics and Dipoles When constructing a capacitor we want to have two plates that are separated by a specific distance. If we just fill the capacitor with air it will work, but it may not stand up to physical abuse. What can we do to solve this problem? We can introduce a different material between the plates to add stability, but we also have to be concerned with how this material will affect the capacitance. What type of material would be appropriate? We know it cannot be a conductor, because we would no longer have a capacitor. This means it should be some sort of insulating material. We call these materials Dielectrics. Dielectrics – Materials that are poor conductors of electricity, but support electric fields. Most materials are dielectrics (wood, glass, ceramic, rubber, plastics, wax, dry air, vacuum, etc.). Dielectrics placed in a capacitor are subjected to an electric field. The electric field causes some amount of polarization by either separation of charges or aligning the dipole molecules contained within the material. Dipole – A single molecule that has an excess positive charge on one side and an excess negative charge on the other. In chemistry they call these polar molecules (water, carbon dioxide, hydrogen chloride, etc.).

We can describe a dipole using a dipole moment, which contains information about the magnitude of the charge, the size of the dipole (separation distance between charges) and the orientation of the dipole. The direction of the dipole vector is from negative to positive, to show how an electric field would affect the molecule. The dipole moment is a vector quantity since it contains information on magnitude and direction. +q P – dipole moment 2a If we place a dipole molecule in an electric field, what will happen? p The dipole will align itself with the external electric field. -q The equal magnitude, but oppositely directed forces will cause the dipole to rotate about a point halfway between the two charges. This means that the dipole experiences a torque. E F a F a a F a O Work is done by the electric field on the dipole to rotate it causing a decrease in the stored potential energy. F

If the dielectric we use to fill the capacitor contains dipole (polar) molecules, let us examine how this will affect the capacitance. Non-polar material The polarized materials can be modeled as if there is a charged plate on either side of the dielectric. The induced surface charge density (sind) is less than the surface charge density (s) of the original plates. Hence, the induced electric field (Eind) is less than the initial electric field (E0). The total electric field (E) between the plates of a capacitor containing a dielectric would then be given by: The magnitude of Eind depends on how much polarization can occur in the dielectric. Polar material – made up of dipoles This means that the strength of the electric field for the capacitor with a dielectric must be some fraction of the strength of the electric field without the dielectric. We introduce a new quantity called the Dielectric Constant to represent this ratio of electric field strengths.

Magnitude of Electric field without dielectric k – dielectric constant The dielectric constant is not really a constant! Magnitude of Electric field with dielectric If we want to relate this to a capacitor it is usually more convenient to discuss the potential difference between the plates than the electric field. The dielectric constant can also be written as the ratio of the potential differences. We can now relate the capacitances with and without the dielectric. We can then rewrite the capacitance for a parallel plate capacitor with a dielectric as: The capacitance with the dielectric is larger since k>1.

Maximum voltage rating Above is a selection of common capacitors used in electric circuits. Each of these capacitors use some type of dielectric. When the dielectric is subjected to an electric field we get polarization, but if the electric field is too strong the dielectric can “breakdown” and the capacitor will no longer function as expected. The potential difference across the plates of the capacitor determines the strength of the electric field. Therefore all capacitors have a maximum voltage rating. When exceeded this may ruin the capacitor and even cause it to explode. The maximum electric field that a dielectric can support without breaking down is called the Dielectric Strength. When you exceed the dielectric strength of a material it begins to conduct. Rubber can conduct if you exceed the dielectric strength. Air conducts when you exceed the dielectric strength. (e.g. Lightning)

it would have been if the dielectric were left in place. A dielectric is inserted between the plates of a capacitor. The system is then charged and the dielectric is removed. The electrostatic energy stored in the capacitor is 1. greater than 2. the same as 3. smaller than it would have been if the dielectric were left in place. Cwithout < Cwith, so Uwithout > Uwith and DU increases Work must be done to remove the dielectric since it has become polarized. The now polarized dielectric is attracted to the plate of opposite sign and requires a force to remove it. If you do work on the system you are increasing the potential energy. Answer: 1. The dielectric is polarized when it is between the charged plates. The positively charged dielectric surface is attracted to the negatively charged plate, and the negatively charged dielectric surface is attracted to the positively charged plate. Thus, you must do work to remove the dielectric. As a result, the electrostatic energy stored in the capacitor increases when the dielectric is removed.

A parallel-plate capacitor is attached to a battery that maintains a constant potential difference V between the plates. While the battery is still connected, a glass slab is inserted so as to just fill the space between the plates. The stored energy 1. increases. 2. decreases. 3. remains the same. Cwithout < Cwith, so Uwithout < Uwith and DU increases Work is done by the battery to add more charges to the plates and therefore the potential energy increases. The battery does work on the system. Answer: 1.When the glass slab is between the plates, it becomes polarized, thereby decreasing the magnitude of the electric field. In order for the battery to maintain a constant potential difference across the plates, it must do work to deposit more charge on the plates. Thus, work is done on the system and the stored energy increases.