Chapter 24 - Electrostatic Energy and Capacitance

Chapter 24 - Electrostatic Energy and Capacitance ● Electric Potential Energy - Occurs due to a collection of point charges o Due to work done in assembling the charges - a sum of the Q1 - Experiences terms (no work needed - comes in for free since there are no other charges present) Q2 - Experiences Q3 - Experiences Q4 - Experiences o So, system potential is (sum of all works) o Note: Each new charge coming in experiences a larger than the previous one. o Now consider the - we get a nice summation. (half of all of permutations). For example above, this chart represents all of the combinations of , which when added up make combination is presented here twice: , as each o Thus, the resulting summation expression: ▪ Since this is for an arbitrary collection of charges, for a continuous charge distribution (i.e. - charges on a conductor), then where is the total charge and is the final CAPACITANCE ( ) -It is a property of a conducting object. .Note potential relative to ● . capacitance is a constant for a certain surface (i.e. - whatever you do to (double, halve, etc.), the same happens to o as well). It measures how much charge an object can hold at a given potential. Generally it's related to the size of the conductor. o SI Unit - Farad (F) - huge unit MORE CASES!!! A spherical capacitor Parallel Plates Surface area of one side of one of the plates - Cylindrical Capacitor Radii small and large note that Specifically for AP part II problems, be able to link the cases we've done so far using the following equations in order: Capacitors in Circuits - schematic symbol: . ● In a circuit, typically we use parallel plate capacitors. ● When connecting a capacitor to a battery: Charge will flow until potential is Note: red arrows indicate flow of equal in both (almost instantly) . Hence, an electrons electric field forms between the two plates until of the capacitor on is met. ● conditi Charge will flow until . At this point, we can calculate - amount of on the plate (i.e. moved around on the circuit) using the definition of capacitance. ● Note total charge on a parallel plate capacitor is always zero ( and ● on one plate on the other plate). When we combine capacitors in series (i.e. - end to end), the voltage across the entire thing will be as if there were one capacitor (i.e. - the voltage of the battery). ● Note how the inside bit is isolated and separate. ● There is the same amount of charge on each capacitor, regardless of size , as when one electron gets bumped off of one capacitor, it goes on to the next one, and the charges cause it to continue along the circuit. ● ● ● Energy in a capacitor - combining (we can do this because it's a continuous charge distribution) and yields in various circuit setups. Capacitors in series "see" less voltage than the battery o offers. The total potential across both capacitors equals the battery equilibrium. , but at since the charge lost from one capacitor goes on the other. o Also, we can express thus ● . , where s cancel. Thus: , . o i.e. - more capacitors in series yields a smaller equivalent o Each capacitor sees less voltage and thus stores less charge. . Capacitors in parallel o All capacitors see the same amount of voltage o So total charge moved by battery gets distributed across all capacitors. Since , and thus , since and Dielectrics ● Dielectrics are materials that fill the gap in a capacitor. ● Generally, we use a better insulator than air (so you can apply a higher voltage without capacitor plates sparking and discharging (called dielectric breakdown)). ● Air breaks down at . ● Dielectric Constant - property of a dielectric. It's a factor by which capacitance increases (represented by the Greek letter kappa - ) ● Replace the original ● Thus, and with in your expressions. . Strengthens capacitance and weakens electric field. o Inside the dielectric, the sum of charges isn't too large, so within the volume of the capacitor, the is less (so thus it is harder to get a spark). Note that this means that the space between the dielectric and one of the plates is going to be more. Charges on plate and dielectric (one side) are not equal and opposite. o Capacitor + Battery = Constant o When an insert dielectric undergoes polarization and is attracted into the gap, the work done decreases potential energy of the capacitor (initially at least). o Battery compensates - battery puts more charges on plates o Final result - Goes back to original energy but there is more charge (effectively increasing the capacitance). ● Isolated capacitor at potential o ● is constant (because of isolation) o If you insert a dielectric... o System potential energy decreases so Some dielectrics o Air - o Oil - o Paper - o Glass across the capacitor decreases.