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Electric Potential

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”.

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Electric Potential

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  1. Electric Potential

  2. 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”

  3. How does this Relate to E-Fields and Forces? • E-Fields • Will provide a force on a charged particle • F=EQ • Electric Potential—Defined as the amount of work done (per unit charge) to move a charged particle from infinity to that specific point • r at infinity=∞ (Dividing by infinity gives you zero) • Electric Potential does have a sign • Depends on direction of the E-Field • Depends on charge of particle

  4. Visual Analogy

  5. Gravitational Anology • Electric Potential is essentially a point in space • Similar to height • Just as a certain h correlates to a certain gravitational potential energy, a certain electric potential (V) correlates to a certain electric potential energy • ∆h= • ∆V=

  6. 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

  7. Relevant Equations Work done by an e-field can be found by determining the displacement of the particle dW=F∙ds dW=qE∙ds W=q ∆𝑉=-

  8. Electric Potential Difference

  9. What Is a Electric Potential Difference? • There are areas of low potential and high potential (depend on location) • The difference in potential between two areas is called the electric potential difference (Denoted by ∆V) • - • Measured in Volts • Because Volts is Joules/Coloumbs, a one coloumb charge will gain one joule when the ∆V=1

  10. 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???????

  11. 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?

  12. 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)

  13. Capacitance

  14. 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

  15. 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

  16. 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=εEA/V V=Ed Substitute V with Ed C=εEA/Ed C=εA/d Finally we add a k to account for the dielectric constant, so the final formula looks like this: C=kεA/d

  17. 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

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

  19. Spherical Capacitors • Same idea as the cylindrical capacitor, but with an area of 4πr2

  20. Derivation E=q/4πr2ε V=∫Ed V=q/4πε∫dr/r2 (Again integrate from b to a with regards to the area of sphere) V=q/4πε(1/a -1/b) C=4πε(ab/b-a)

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