## Uniform Electric Field (3 of 9) Potential Difference due to Parallel Plates: An Explanation

okay in today's video we are going to be

talking about electric potential

difference and we're gonna be

specifically talking about electric

potential difference as it relates to

parallel plates and not necessarily

point charges parallel plates are

different because they have a uniform

electric field so we have these two

parallel plates one positively charged

ones negatively charged and we have a

charged some negatively charged object

and electron or some other negatively

charged object that we're going to be

moving between those plates now before

we talk specifically about potential and

potential difference I just want to

point out that there are these terms

electric potential energy electric

potential and potential difference that

all sound very similar but some of these

things are very different from each

other

specifically electric potential energy

is measured in joules okay just like any

kind of potential energy or any kind of

energy electric potential energy is

measured in joules we say electric

potential energy or the change in

electric potential energy we don't say

electric potential energy difference

you'll notice over here we have electric

potential usually referred to as just

potential and potential difference

sometimes referred to as electric

potential difference these are measured

in joules per Coulomb which we call the

volt all right

so these have this word or just referred

to often as potential and potential

difference this is electric potential

energy or we would say the change in

electric potential energy not electric

potential energy difference okay so

those terms are different from each

other and hopefully we'll get a sense

about how they're different and how

they're related in this video now

electric potential difference the

definition for electric potential

difference is this it's the change in

potential energy per unit of charge so

here we have this charge which we can

move back and forth between these plates

and we're gonna figure out the potential

difference and the potential difference

is the change in potential energy of

this charge per unit of this charge and

we write that down mathematically like

this potential has the symbol V

potential difference is Delta V this

triangle means we say this Delta which

means the change in potential and as our

equation says the change in potential

potential difference is equal to the

change in potential energy Delta UE the

change in electric potential energy

divided by the amount of charge that we

move between those plates now potential

energy has the unit Joule charge is a

Coulomb joules per Coulomb so the unit

for potential difference is a Joule per

Coulomb but we abbreviate Joule per

Coulomb has the Volt and we write that

as an abbreviation as V so wine volt

which we abbreviate as V is one Joule

per Coulomb all right now this is the

definitions we write outwards this is

the definition as we write it out as an

equation and this is a very important

equation which you should remember but

if you're taking ap physics that this

equation written out like this is on

your equation sheet and basically this

says that the change while we did was

cross multiply and solve for the change

in potential energy so the change in

electric potential energy is equal to

the amount of charge and the potential

difference to which that charge is moved

so if we take this charge and we move it

from the positive plate quite wants to

be to the negative plate where it

doesn't want to be we have to apply a

force over a distance and we move that

charge through that potential difference

and we get the amount of electric

potential energy or the change in

electric potential energy now also if we

move that charge and gave it potential

energy we must have done some work on

that charge so the change in potential

energy as you should remember from

mechanics and conservation of energy is

also equal to the work we did is also

equal to the potential

energy change which therefore is also

equal to the amount of charge and the

potential difference through which is

moved so you can figure out how much

work you did in giving that charge that

much potential energy or how much work

you did in moving that charge through

that potential difference okay

now the charge is there if we release it

it doesn't want to be there it's going

to move back down so to speak and

therefore it's going to be losing some

potential energy that comes back where's

that potential energy go once again

through mechanics and conservation of

energy you should remember that that's

equal to if as the charge loses

potential energy it's going to be

converted into kinetic energy so the

amount of kinetic energy that it would

gain as it moves back would be again

equal to the amount of charge times the

potential difference okay now once again

this equation is on your equation sheet

these two equations are not but you

should remember based on your

relationships for mechanics and for

conservation of energy that all three of

these things are is kind of like

essentially equal to each other all

right now at the end of this video I'm

going to put some links to some other

videos I made going through these

mathematical and these relationships so

that you get a better feel for how these

things work with parallel plates it's

good to practice a few problems it'll

give you a sense conceptually and

mathematically about how those things

work okay we did that now we're going to

do one more thing in order to do that

we're going to go back to our definition

of mechanical of a potential difference

the potential difference is equal to

change in potential energy per unit of

charge now in a previous video I went

through and showed you how to calculate

the change in potential energy and one

way we can do that is the change in

potential energy is equal to the amount

of charge the electric field strength is

for the electric field so the magnitude

of the electric field and again we have

a uniform electric field and

distance between the plates so now what

I'm going to do is I'm going to

substitute the QED for the change of

potential energy in this equation in our

definition and we get that the potential

difference is equal to the change of

potential energy which we can calculate

QED divided by the amount of charge this

Q and this Q are at this chart so they

are the same charge so we can we can

cancel these two and we basically

dividing out two charge so you get from

that that the change in potential

between those two plates the potential

difference between those two plates is

simply equal to the electric field

strength times the distance between the

plates okay and you will notice that the

change in potential energy is equal to

the amount of charge give me is directly

related to the amount of charge but the

potential difference between parallel

plates is only related to the electric

field strength and the distance and the

distance between those plates this

equation you can only use for parallel

plates because in order to use this

equation you have to have a uniform

electric field with parallel plates you

have a uniform electric field with point

charges you do not have a uniform

electric field okay that's very

important parallel plates uniform

electric field you can use this equation

now this equation is also on your

physics AP Physics equation shoot except

it's not written like this it's written

like this that the electric field is

equal to the potential difference

divided by what they call Delta R and

Delta R is the separation between the

plates but it simply also refers to the

distance between the plates so this

equation is important one to keep in

mind but it's written like this on your

AP Physics equation sheet especially for

the new AP Physics 2002

13 2014 equation sheet on the old sheet

it says D down here but it's the same

thing

Delta R is the separation between the

plates now let's look at this I think

this is another very interesting thing

bolts potential difference is measured

in bolts distance separation is measured

in meters that means that in this case

the electric field has the units volts

per meter well you should remember

earlier we said that electric field has

the units Newton's per Coulomb and

that's what it is by definition the

Newton's of force per Coulomb of charge

well how come it's both per meter well

volts per meter is equal to Newton per

Coulomb and this is how that works this

is another fascinating aspect of this

topic volts is joules per Coulomb so we

can kind of look at expand a volt into a

Joule per Coulomb well Joule per Coulomb

is also a Newton meter

okay so joules can be expanded into a

Newton meter so now we have Newton meter

per Coulomb we have meter here and meter

up here and those meters will cancel and

we're left with simply left with

Newton's per Coulomb so electric field

the units are Newton's per Coulomb and a

volt per meter is the same thing as a

Newton per Coulomb okay so that's how

those things work all right so we did a

lot in this video I think one of the

main things is we talked about the

definition this is the equation we use

for the definition the potential

difference is equal to the change of

potential energy electric potential

energy divided by the unit of charge

equation is on your AP Physics web sheet

the equation sheet is also equal to the

amount of work and the change in kinetic

equation how we can use this equation to

figure out the potential difference or

in this case the electric field but that

this equation can only be used for

parallel plates which have a uniform

electric field okay thank you for

watching here are the links to those

other videos where you can do

do a few simple problems and do some

practice on calculating potential

difference work kinetic energy and

separation between the plates okay so

thank you for watching I hope you found

that helpful if you did give me a thumbs

up or leave me a comment yes or no did

you like that was that helpful in the

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and we will see you in the next video