ELECTRIC POTENTIAL

WHAT IS A ELECTRIC POTENTIAL? Amount of electric potential energy something has at a certain point in space Electric Potential is a scalar (does NOT have direction) Measured in Joules/Coulombs  More commonly known as Volts Denoted by “V” or “∆V”

HOW DOES THIS RELATE TO E-FIELDS AND FORCES?

VISUAL ANALOGY

GRAVITATIONAL ANOLOGY

EQUIPOTENTIAL LINES Denote where a certain Electric Potential Energy occurs inside an electric field Lines are drawn perpendicularly to E-Field Lines Similar to a topographic Map

RELEVANT EQUATIONS

ELECTRIC POTENTIAL DIFFERENCE

WHAT IS A ELECTRIC POTENTIAL DIFFERENCE?

HOW DOES THIS RELATE TO CIRCUITS? Charges move in circuits How do we move charges????? WE DO WORK What happens when we do work on an electric charge?????? THERES A DIFFERENCE IN ELECTRIC POTENTIAL What happens in a circuit????? CHARGES MOVE So???????

MORE ABOUT CIRCUITS Conventional current flow is out of the positive and to the negative Particle starts at area of high potential and ends at the area of low potential Where is low and where is high potential?

BATTERIES Batteries simply provide the energy needed to do the work to move the current from high potential to low potential Positive node is area of high potential Negative node is area of low potential This creates a potential difference across the battery This is its voltage!!! Remember Ohm’s law (V=IR)

CAPACITANCE

WHAT IS A CAPACITANCE? Capacitors are used to store charge as potential energy in an E-field Potential energy is created inside the capacitor, but not outside Capacitors are charged by an electric current After the capacitor is charged, then it can be used as a source of energy Each plate is a Gaussian surface IMPORTANT FORMULA C=q/V

DIELECTRIC CONSTANT, AREA, AND DISTANCE The dielectric constant is the insulator between the two plates of the capacitor that limits the potential difference between the two plates. The area of the capacitor is the area of the positive plate of the capacitor. The plate is where the ions build up and when the plate is completely filled with ions, the other plate is polarized by the ions and the capacitor is fully charged (I total=0) Distance refers to the distance between the plates, and is an inverse relation of capacitance

GAUSS AND CAPACITORS By using Gauss’ formula and the formula for capacitance we can find the formula for the Capacitor Gauss: EA=q/ ε C= ε EA/V V=Ed Substitute V with Ed C= ε EA/Ed C= ε A/d Finally we add a k to account for the dielectric constant, so the final formula looks like this: C=k ε A/d

CYLINDRICAL CAPACITORS We know from Gauss that flux only exists through the sides of a cylinder, and not the end caps of a cylindrical object So to find the cylindrical capacitors formula we must integrate with regards to radius

DERIVATION E=q/(2 πε Lr) V=∫Ed V= -q/(2 πε L) ∫dr/r (integrate from b to a with regards to radius of inner and outer shell) V=q/(2 πε L) ln(b/a) Therefore… C=2 πε (L/ln(b/a))

SPHERICAL CAPACITORS Same idea as the cylindrical capacitor, but with an area of 4 π r 2

DERIVATION E=q/4 π r 2 ε V=∫Ed V=q/4 πε ∫dr/r 2 (Again integrate from b to a with regards to the area of sphere) V=q/4 πε (1/a -1/b) C=4 πε (ab/b-a)