ELECTRIC POTENTIAL. WHAT IS A ELECTRIC POTENTIAL? Amount of electric potential energy something has at a certain point in space Electric Potential is.

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 VoltsDenoted by “V” or “∆V”

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

VISUAL ANALOGY

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=

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

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=-

ELECTRIC POTENTIAL DIFFERENCE

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

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 DISTANCEThe 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=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

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/(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))

SPHERICAL CAPACITORS

Same idea as the cylindrical capacitor, but with an area of 4πr2

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)