Electricity and magnetism
Electric Potential Energy Introduction to electric potential
Electric Potential Energy
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- Let's review a little bit of what we had learned many, many
- videos ago about gravitational potential energy and then see
- if we can draw the analogy, which is actually very strong,
- to electrical potential energy.
- So what do we know about
- gravitational potential energy?
- If we said this was the surface of the Earth-- we
- don't have to be on Earth, but it makes visualization easy.
- We could be anywhere that has gravity, and the potential
- energy would be due to the gravitational field of that
- particular mass, but let's say this is the
- surface of the Earth.
- We learned that if we have some mass m up here and that
- the gravitational field at this area-- or at least the
- gravitational acceleration-- is g, or 9.8 meters per second
- squared, and it is h-- we could say, I guess, meters,
- but we could use any units.
- Let's say it is h meters above the ground, that the
- gravitational potential energy of this object at that point
- is equal to the mass times the acceleration of gravity times
- the height, or you could view it as the force of gravity,
- the magnitude of the force of gravity.
- You know, it's a vector, but we can say the magnitude of
- the vector times height.
- And so what is potential energy?
- Well, we know that if something has potential energy
- and if nothing is stopping it and we just let go, that
- energy, at least with gravitational potential
- energy, the object will start accelerating downwards, and a
- lot of that potential energy, and eventually all of it, will
- be converted to kinetic energy.
- So potential energy is energy that is being stored by an
- object's situation or kind of this notional energy that an
- object has by virtue of where it is.
- So in order for something to have this notional energy,
- some energy must have been put into it.
- And as we learned with gravitational potential
- energy, you could view gravitational potential energy
- as the work necessary to move an object to that position.
- Now, if we're talking about work to move something into
- that position, or whatever, we always have to think about,
- well, move it from where?
- Well, when we talk about gravitational potential
- energy, we're talking about moving it from the surface of
- the Earth, right?
- And so how much work is required to move that same
- mass-- let's say it was here at first-- to move it from a
- height of zero to a height of h?
- Well, the whole time, the Earth, or the force of
- gravity, is going to be F sub g, right?
- So essentially, if I'm pulling it or pushing it upwards, I'm
- going to have to have-- and let's say at a constant
- velocity-- I'm going to have to have an equal and opposite
- force to its weight to pull it up.
- Otherwise, it would accelerate downwards.
- I'd have to do a little bit more just to get it moving, to
- accelerate it however much, but then once I get it just
- accelerating, essentially I would have to apply an upward
- force, which is equivalent to the downward force of gravity,
- and I would do it for a distance of h, right?
- What is work?
- Work is just force times distance.
- Force times distance, and it has to be force in the
- direction of the distance.
- So what's the work necessary to get this mass up here?
- Well, the work is equal to the force of gravity times height,
- so it's equal to the
- gravitational potential energy.
- Now this is an interesting thing.
- Notice we picked the reference point as the surface of the
- Earth, but we could have picked any
- arbitrary reference point.
- We could have said, well, from 10 meters below the surface of
- the Earth, which could have been down here, or we could
- have actually said, you know, from a platform that's 5
- meters above the Earth.
- So it actually turns out, when you think of it that way, that
- potential energy of any form, but especially gravitational
- potential energy-- and we'll see electrical potential
- energy-- it's always in reference to some other point,
- so it's really a change in potential energy that matters.
- And I know when we studied potential energy, it seemed
- like there was kind of an absolute potential energy, but
- that's because we always assume that the potential
- energy of something is zero the surface of the Earth and
- that we want to know the potential energy relative to
- the surface of the Earth, so it would be kind of, you know,
- how much work does it take to take something from the
- surface of the Earth to that height?
- But really, we should be saying, well, the potential
- energy of gravity-- like this statement shouldn't be, you
- know, this is just the absolute
- potential energy of gravity.
- We should say this is the potential energy of gravity
- relative to the surface of the Earth is equal to the work
- necessary to move something, to move that same mass, from
- the surface of the Earth to its current position.
- We could have defined some other term that is not really
- used, but we could have said potential energy of gravity
- relative to minus 5 meters below the surface of the
- Earth, and that would be the work necessary to move
- something from minus 5 meters to its current height.
- And, of course, that might matter.
- What if we cut up a hole and we want to see what is the
- kinetic energy here?
- Well, then that potential energy would matter.
- Anyway, so I just wanted to do this review of potential
- energy because now it'll make the jump to electrical
- potential energy all that easier, because you'll
- actually see it's pretty much the same thing.
- It's just the source of the field and the source of the
- potential is something different.
- So electrical potential energy, just actually we know
- that gravitational fields are not constant, we can assume
- they're constant maybe near the surface of the Earth and
- all that, but we also know that electrical fields aren't
- constant, and actually they have very simple formulas.
- But just for the simplicity of explaining it, let's assume a
- constant electric field.
- And if you don't believe me that one can be constructed,
- you should watch my videos that involve a reasonable bit
- of calculus that show that a uniform electric field can be
- generated by an infinite uniformly charged plane.
- Let's say this is the side view of an infinite uniformly
- charged plane and let's say that this
- is positively charged.
- Of course, you can never get a proper side view of an
- infinite plane, because you can never kind of cut it,
- because it's infinite in every direction, but let's say that
- this one is and this is the side view.
- So first of all, let's think about its electric field.
- It's electric field is going to point upward, and how do we
- know it points upward?
- Because the electric field is essentially what is-- and this
- is just a convention.
- What would a positive charge do in the field?
- Well, if this plate is positive, a positive charge,
- we're going to want to get away from it.
- So we know the electric field points upward and we know that
- it's constant, that if these were field vectors, that
- they're going to be the same size, no matter how far away
- we get from the source of the field.
- And I'm just going to pick a number for the
- strength of the field.
- We actually proved in those fancy videos that I made on
- the uniform electric field of an infinite, uniformly charged
- plane that we actually proved how you could calculate it.
- But let's just say that this electric field is equal to 5
- newtons per coulomb.
- That's actually quite strong, but it makes the math easy.
- So my question to you is how much work does it take to take
- a positive point charge-- let me pick a different color.
- Let's say this is the starting position.
- It's a positive 2 coulombs.
- Once again, that's a massive point charge, but
- we want easy numbers.
- How much work does it take it to move that 2-coulomb charge
- 3 meters within this field?
- How much work?
- So we're going to start here and we're going to move it
- down towards the plate 3 meters, and it's ending
- position is going to be right here, right?
- That's when it's done.
- How much work does that take?
- Well, what is the force of the field right here?
- What is the force exerted on this 2-coulomb charge?
- Well, electric field is just force per charge, right?
- So if you want to know the force of the field at that
- point-- let me draw that in a different color.
- The force of the field acting on it, so let's say the field
- force, or the force of the field, actually, is going to
- be equal to 5 newtons per coulomb times 2 coulombs,
- which is equal to 10 newtons.
- We know it's going to be upward, because this is a
- positive charge, and this is a positively charged infinite
- plate, so we know this is an upward force of 10 newtons.
- So in order to get this charge, to pull it down or to
- push it down here, we essentially have to exert a
- force of 10 newtons downwards, right?
- Exert a force of 10 newtons in the direction of the movement.
- And, of course, just like we did with gravity, we have to
- maybe do a little bit more than that just to accelerate
- it a little bit just so you have some net downward force,
- but once you do, you just have to completely balance the
- upward force.
- So just for our purposes, you have a 10-newton force
- downward and you apply that force for a distance of 3
- meters, the work that you put to take this 2-coulomb charge
- from here to here, the work is going to be equal to 10
- newtons-- that's the force-- times 3 meters.
- So the work is going to equal 30 newton-meters, which is
- equal to 30 joules.
- A joule is just a newton-meter.
- And so we can now say since it took us 30 joules of energy to
- move this charge from here to here, that within this uniform
- electric field, the potential energy of the charge here is
- relative to the charge here.
- You always have to pick a point relative to where the
- potential is, so the electrical potential energy
- here relative to here and this is electrical potential
- energy, and you could say P2 relative to P1-- I'm using my
- made-up notation, but that gives you a sense of what it
- is-- is equal to 30 joules.
- And how could that help us?
- Well, if we also knew the mass-- let's say that this
- charge had some mass.
- We would know that if we let go of this object, by the time
- it got here, that 30 joules would be-- essentially
- assuming that none of it got transmitted to heat or
- resistance or whatever-- we know that all of it would be
- kinetic energy at this point.
- So actually, we could work it out.
- Let's say that this does have a mass of 1 kilogram and we
- were to just let go of it, right?
- We used some force to bring it down here, and then we let go.
- So we know that the electric field is going to accelerate
- it upwards, right?
- It's going to exert an upward force of 5 newtons per
- coulomb, and the thing's going to keep [COUGHS]--
- excuse me-- keep accelerating until it gets
- to this point, right?
- What's its velocity going to be at that point?
- Well, all of this electrical potential energy is going to
- be converted to kinetic energy.
- So essentially, we have 30 joules is going to be equal to
- 1/2 mv squared, right?
- We know the mass, I said, is 1, so we get 60 is equal to v
- squared, so the velocity is the square root of 60, so it's
- 7 point something, something, something meters per second.
- So if I just pull that charge down, and it has a mass of 1
- kilogram, and I let go, it's just going to accelerate and
- be going pretty fast once it gets to this point.
- Anyway, I'm 12 minutes into this video, so I will continue
- in the next, but hopefully, that gives you a sense of what
- electrical potential energy is, and really, it's no
- different than gravitational potential energy.
- It's just the source of the field is different.
- See you soon.
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