Understanding Potential Difference: Work Done per Unit Charge?

[physics kiddy]

I learned Potential but could not understand what Potential Difference is. Some define it as Work Done per unit charge. I am confused what per unit charge is. Does that mean electrons or protons ? As much as I know, electric current is the flow of negatively charged electrons to the positive electrode. But, that's natural and won't require any work to be done on it because unlike charges attract each other. Please explain this concept. Thanks.

 

[sankalpmittal]

I learned Potential but could not understand what Potential Difference is. Some define it as Work Done per unit charge. I am confused what per unit charge is. Does that mean electrons or protons ? As much as I know, electric current is the flow of negatively charged electrons to the positive electrode. But, that's natural and won't require any work to be done on it because unlike charges attract each other. Please explain this concept. Thanks.

Hello physics kiddy,

Listen to my analogy :

We are neglecting the resistance of the wire ok .

Potential difference is defined as the amount of work done in moving a unit *positive* or 1 coulomb of charge from one point to another in an electric circuit.

Ok ,
lets say on Q coulombs of charge W joules of work is done.
So on 1 coulomb of charge W/Q of work will be done.
But work done on 1 coulomb of charge is potential difference.

1 Volt = 1 Joule / 1 coulomb

per unit charge means on 1 coulomb of charge ( or unit positive charge). Per is / sign here.

+7 units charge                                                                                   - 9 units of charge
------------------------------------------------------------------------------------------

The difference between charges is work done or the difference in potential between two points.

V₂-V₁ = W/Q
Original definitions are made on basis of positive charges but that doesn't make sense. Look here : http://amasci.com/amateur/elecdir.html and http://amasci.com/miscon/eleca.html#frkel

Take a metal. Obviously the electrons move but not randomly. This shows that electromotive force is required for their one directional movement. Talking about electrolysis , there has to be unidirectional flow. The force of attraction of two electrodes isn't enough. There exist electromotive force between two terminals of battery.

@ sophiecentaur
So it isn't the Volts that are the Force - it's the Volts per metre. If there is 1,000,000V PD between two plates, separated by 100km, there is still only 1N of force on 1 Coulomb.
P.S. You don't normally (ever) come across any 'object' charged with 1 Coulomb.

Why do we name it electromotive "force" ? Its unit is but Volts. 1 Volt = 1 joule / 1 coulomb.

You say force = 1 joule * 1 metre / 1 coulomb ? That's absurd , I think.

 

[sophiecentaur]

You were told exactly right. When there is a PD of 1Volt and 1 Coulomb has passed, 1 Joule of energy has been transferred. Volts are a Potential Difference in exactly the same way as a height difference corresponds to a change in Gravitational Potential.
So
GPE = mgh (from School)
and
Electrical Potential Energy = QV

"What about the FORCE?" is what people ask.
Gravitational force on a Mass (m) is the rate at which GPE changes with distance. That is actually mg (weight). 1kg 'weighs' 1times g or 9.81N.

The Electric Field is the rate that the Electrical PD changes with distance and, as PD is Volts, the field is in Volts per metre. So 1V over a 1m gap would exert 1N of force on 1 Coulomb.

So it isn't the Volts that are the Force - it's the Volts per metre. If there is 1,000,000V PD between two plates, separated by 100km, there is still only 1N of force on 1 Coulomb.
P.S. You don't normally (ever) come across any 'object' charged with 1 Coulomb.

 

[physics kiddy]

So, shall I conclude that Voltage is based on the convention that protons constitute the flow of electricity ?

 

[sophiecentaur]

So, shall I conclude that Voltage is based on the convention that protons constitute the flow of electricity ?

How could have got that message?
The Definition of One Volt is that One Joule of Energy is transferred when One Coulomb of Charge changes its Potential by One Volt. Just get that sorted out first. The Volt was set long before anyone had the microscopic experience of electrons and you really don't need to consider the little devils when talking about 'Charge', any more than you consider molecules when you are drinking a Pint. 'Positive' and 'Negative' were just signs that someone decided to paint on an early battery and there's no point in changing it now.

IT JUST SO HAPPENS that, in metal wires, the charge is carried by mobile electrons and they happen to have a negative charge (as defined and established long ago). But an electron going in one direction is totally equivalent to a positive charge going in the other direction. Already, 'people' are making groups of AntiHydrogen atoms. It may be only a matter of time before someone makes a circuit of 'AntiCopper', in which the charge is carried by Positrons. Then you'll be happy?

 

[Studiot]

Just remember that two different things are measured in volts.

Potential

Potential difference

This is like saying that the height of Mt Everest is 8850m but the height difference between Mt Everest and Mt Kilimonjaro is 955m - both are measured in metres, but are different.

 

[sophiecentaur]

And, furthermore, knowing your height (above sea level, say) tells you nothing about how well your Hydroelectric System will work until you know the new height to which your water will flow. PD is of much more interest than just plain Potential..

Electric Potential (without the "difference") refers to the energy transferred when a unit charge is brought from an infinite distance to the point of interest. The actual potential of a point in space refers to the total effect of all the charges in space. It's a pretty useless quantity in many respects. It is, in fact, always referred to 'somewhere' and that tends to be Earth (a large body that is handy to strap things to).

@physics-kiddy: Despite your first words on this thread, I think you are more likely to 'understand' PD than Potential, in fact - because it is a more tangible idea.

 

[physics kiddy]

How could have got that message?
The Definition of One Volt is that One Joule of Energy is transferred when One Coulomb of Charge changes its Potential by One Volt.

This definition has confused me ! How can we define volt using volt ?

 

[sankalpmittal]

This definition has confused me ! How can we define volt using volt ?

physics kiddy , there you go : you'll get your answer :
http://en.wikipedia.org/wiki/Volt#Definition
http://en.wikipedia.org/wiki/Voltage

Here is my definition of voltage :
Voltage is just defined as the difference in electric potential energies of charges at any two points in a circuit. It is a common term for electromotive force , potential difference and electric potential as well.

@ sophiecentaur and Studiot

It makes sense to consider the current flowing from positive terminal to negative terminal of battery because mathematics work by this fact. Moreover I don't think that current is flow of electrons in the metallic circuit. Please I know I am going against and correct me if I am wrong.

Current is the flux which is produced due to back attraction force of electrons and positive lattice in metal. When metal atoms loose electrons then there develops a positive charge on them. This positive charge tend to attract electrons back but electrons due to their high speed are not attracted yet an electrodynamic flux is produced between electron and positive ion. That flux is current. Attraction force of this ion is more directed than force by which electron tends to attract it. As positive ion cannot move !

Please read this , I found a very interesting page here : http://amasci.com/miscon/eleca.html#frkel

 

[Bobbywhy]

sankalpmittal, regarding the website page (amasci) you cited as "very interesting" I caution you about trusting everything you find on the internet. The reference you give, written by William J. Beaty, has some extremely controversial and doubtful statements about electricity.

Please learn how to use reliable and trusted sources. One example is to use Michael Shermer's "Baloney Detector". You apply his ten items to a source and the results help you decide it the source is beleivable or not. Check it out: http://homepages.wmich.edu/~korista/baloney.html

Also you may use "Carl Sagan's Baloney Detection Kit" at: http://www.carlsagan.com/index_ideascontent.htm

Lastly, trust no one who claims "Newton was mistaken" or "The 2nd Law of Thermodynamics is wrong", or "most textbooks say...,but the real truth is ..."

 

[sophiecentaur]

This definition has confused me ! How can we define volt using volt ?

As in " the metre is the distance between two points, separated by one metre"?
Self referencing is not a definition of something.

 

[mikeph]

I learned Potential but could not understand what Potential Difference is. Some define it as Work Done per unit charge. I am confused what per unit charge is. Does that mean electrons or protons ? As much as I know, electric current is the flow of negatively charged electrons to the positive electrode. But, that's natural and won't require any work to be done on it because unlike charges attract each other. Please explain this concept. Thanks.

You are pretty close.

Potential is defined at a point in a circuit.

Potential difference is defined at a PAIR of points in a circuit, (as the two individual potentials subtracted).The height analogy is good; if I tell you Everest is 8848m high you will say "ok, what does that mean?" because a length is meaningless without a reference point. If you say "it is 8848m above sea level" then that makes sense. It's the same with voltage. If you say "the potential here in a circuit is 3.2V" then it doesn't make sense. If you say "the potential difference across this light bulb is 3.2V" then it makes sense: the voltage across it is 3.2V.

ie. 1 coulumb of electrons will expend 3.2 J of energy when they move across the bulb.

 

[sophiecentaur]

You are pretty close.

Potential is defined at a point in a circuit.

Potential difference is defined at a PAIR of points in a circuit, (as the two individual potentials subtracted).

And how would you actually measure that potential? With a lead to outer space? No. What you are calling Potential is the PD BETWEEN your point and another arbitrarily selected point, somewhere else on EARTH. It is still a Potential Difference. Potential and PD are not only quantities in a Circuit.

The height analogy is good; if I tell you Everest is 8848m high you will say "ok, what does that mean?" because a length is meaningless without a reference point. If you say "it is 8848m above sea level" then that makes sense. It's the same with voltage. If you say "the potential here in a circuit is 3.2V" then it doesn't make sense. If you say "the potential difference across this light bulb is 3.2V" then it makes sense: the voltage across it is 3.2V.

OK, here- you are making the point that 'difference is what counts'. The only time one could argue that it doesn't is when charged particles fall out of space onto a planet with a non-zero net charge..

ie. 1 coulumb of electrons will expend 3.2 J of energy when they move across the bulb.

But WHY? do you insist on using the word "Electrons" here? How many electrons will actually get all the way from input to output terminal of a circuit when a Coulomb passes? Are we to have an entirely different description when we are dealing with an electro-plating circuit when positive metal ions flow to the Cathode and negative Ions could be flowing towards the Anode? The word that includes all possible scenarios is CHARGE so why not use it?.
I thought that PF had some sort of aim to get people thinking in the most fruitful way (note, I haven't used the word "right") in order to stand a chance of improving their understanding. Why perpetuate the misconceptions that naff Science teachers bombard kids with?

If a contributor asks for a definition of the Volt but inappropriately specifies exactly the terms in which the definition should be made then, perhaps, it is up to Him to make the compromises and to come to terms with things and not up to someone to bend the facts in order to make him happy.

The 'consumer society' doesn't always apply and the customer isn't always right.

 

[physics kiddy]

You are pretty close.

Potential is defined at a point in a circuit.

Potential difference is defined at a PAIR of points in a circuit, (as the two individual potentials subtracted).


The height analogy is good; if I tell you Everest is 8848m high you will say "ok, what does that mean?" because a length is meaningless without a reference point. If you say "it is 8848m above sea level" then that makes sense. It's the same with voltage. If you say "the potential here in a circuit is 3.2V" then it doesn't make sense. If you say "the potential difference across this light bulb is 3.2V" then it makes sense: the voltage across it is 3.2V.

1 coulumb of electrons will expend 3.2 J of energy when they move across the bulb.

I am close to the answer but every time I get confused why 1 coulomb of electrons expend energy when they move across the bulb. That's something natural and won't require work. How's that possible ?

 

[Alephu5]

I am close to the answer but every time I get confused why 1 coulomb of electrons expend energy when they move across the bulb. That's something natural and won't require work. How's that possible ?

For a simplistic understanding of electricity, you can imagine it as water running through pipes. The voltage is the result of an imbalance in the circuit; the negative end of a cell has an excess of electrons, whilst the positive end does not have enough to be electrically stable. This is equivalent to putting pressure into a pipe that is blocked off.

Once you remove the blockage the water will flow until it reaches equilibrium, this is equivalent to putting the cell in a closed circuit and letting it run flat. Essentially you can think of voltage as the pressure in the pipe and resistance as the pipe diameter.

Conservation of energy means that you lose energy when you pass current through a bulb, it is sort of like having a small hole somewhere in the pipe. (Considering no electrons actually leave the circuit it would probably be more accurate to describe a water wheel or something that obstructs flow.) I hope this shed's light on why electrons lose energy as they pass through a component.

 

[sophiecentaur]

I am close to the answer but every time I get confused why 1 coulomb of electrons expend energy when they move across the bulb. That's something natural and won't require work. How's that possible ?

If you lift a mass against gravity, you put energy in. If it falls, you get energy out. With charge, if a +charge flows from + to -, you get energy out, if it flows from - to +, you have put energy in. One way is, as you say, "natural", the other needs you do 'do something'. But either way, energy is 'transferred'.

 

[rcgldr]

I am close to the answer but every time I get confused why 1 coulomb of electrons expend energy when they move across the bulb. That's something natural and won't require work. How's that possible ?

Going back to the gravitational analogy, if you lower a weight by some height and then hold it still, it's kinetic energy hasn't changed, but it's gravitational potential energy is less than it was before because of the reduced height.

 

[sophiecentaur]

If you lower a mass and it is stationary at the bottom then you must have taken that GPE and used it to, perhaps, heat up a brake or move a clock mechanism. The Energy has to go somewhere or come from somewhere Always. Current will flow through a wire without dissipating much energy (low resistance) and the PD will be small. Across a motor / lamp / heater the energy is transferred so the PD is high.

 

[rcgldr]

If you lower a mass and it is stationary at the bottom then you must have taken that GPE and used it to, perhaps, heat up a brake or move a clock mechanism. The Energy has to go somewhere or come from somewhere Always. Current will flow through a wire without dissipating much energy (low resistance) and the PD will be small. Across a motor / lamp / heater the energy is transferred so the PD is high.

The analogy I was trying to convey was that the decrease in potential across motor / lamp / heater is similar to a decrease in GPE due to a decrease in height. I wasn't trying to convey the magnitude of that decrease. I should have clarified that energy can be extracted by reducing potential energy even if kinetic energy isn't changed.

 

[sophiecentaur]

I appreciate that but the OP seems not to get the significance of energy conservation laws.

 

[nsaspook]

sankalpmittal, regarding the website page (amasci) you cited as "very interesting" I caution you about trusting everything you find on the internet. The reference you give, written by William J. Beaty, has some extremely controversial and doubtful statements about electricity.

What is "doubtful' about Mr. Beaty's statements on electricity?

 

[sophiecentaur]

What is "doubtful' about Mr. Beaty's statements on electricity?

I must say, I tend to agree with your query. What Mr B. writes is fairly chatty but I would need to have individual 'doubts' spelled out as most of it is a lot less 'doubtful than many statements I've read on threads like this one.
The one really good point that he makes is that the term 'Electricity' is a catch-all and is not really defined at all. When anyone talks about "Electricity flowing" or "Electricity going into..." I realize they are on very thin ice - yet they still try to 'explain' things to other people.

I also agree with him that it would have done us no favours at all if the electron had turned out to have a charge that's defined as positive because it would have allowed even MORE sloppy and over-simplified thinking.

 

[mikeph]

sophiecentaur- I appreciate you're trying to help but nitpicking my every comment is having the opposite effect. My idea is to give a basic conceptual explanation which someone can pick up and work with.

Nobody is saying charge MUST be an electron but I am not writing a rigorous paper, I am talking in examples. Nor am I trying to suggest that a circuit is the only place a potential can exist, again it's a simple example. I had the exact same problem of not understanding voltage at school and my teacher was hopeless to explain it to me. All I wanted was an idea I could work with in my head and I never got it.

The rigour can come later... the idea is key

 

[sophiecentaur]

sophiecentaur- I appreciate you're trying to help but nitpicking my every comment is having the opposite effect. My idea is to give a basic conceptual explanation which someone can pick up and work with.

Nobody is saying charge MUST be an electron but I am not writing a rigorous paper, I am talking in examples. Nor am I trying to suggest that a circuit is the only place a potential can exist, again it's a simple example. I had the exact same problem of not understanding voltage at school and my teacher was hopeless to explain it to me. All I wanted was an idea I could work with in my head and I never got it.

The rigour can come later... the idea is key

But, if you bother to read through Mr. Beaty's long web page (and I agree with pretty much all of it), you will see that the idea that you are trying to sell is too dodgy to risk passing on to anyone else. Just, for a minute, consider that it may all be very different and more complicated than your idea can address. I can accept that you may have used this idea to help you, personally, to get somewhere beyond it. However, I have read and heard too much rubbish from people who's only concept of Electricity is based around that sort of idea and they have to 'unlearn' it before they can progress. The 'wrong' model can't be justified when there are others which are safer. I'm not just nitpicking - I am really concerned that people will get the wrong idea as a result of some of what you are telling them. When you give advice, you have to accept responsibility at the same time. Your teacher was clearly an example of someone who had a 'satisfactory' personal model which blighted your personal learning - so I hope you can see where I'm coming from.

 

[Bobbywhy]

I have revisited the site about “Electricity Misconceptions” written by William J. Beaty. After careful reading it became clear that he describes the mechanisms of electricity correctly. On my first visit there I did not spend enough time to carefully study and learn from it. Then I made a fast, uninformed and incorrect decision to criticize his work.

Thanks to all of you here who questioned my doubt. Your questioning motivated me to reexamine the web page. In fact, I now recommend his web page to all who want to get a clear and concise explanation of the mechanisms of electricity. I apologise for my mistake in pre-judging William J. Beaty.

Bobbywhy

http://amasci.com/miscon/eleca.html#frkel

 

[physics kiddy]

And how would you actually measure that potential?
I thought that PF had some sort of aim to get people thinking in the most fruitful way (note, I haven't used the word "right") in order to stand a chance of improving their understanding. Why perpetuate the misconceptions that naff Science teachers bombard kids with?

If a contributor asks for a definition of the Volt but inappropriately specifies exactly the terms in which the definition should be made then, perhaps, it is up to Him to make the compromises and to come to terms with things and not up to someone to bend the facts in order to make him happy.

The 'consumer society' doesn't always apply and the customer isn't always right.

Now, I feel I am close to the answer. With a little help, I would be able to clear my doubts and know the truth. Surely, I am not thinking the most scientific way but I won't be able to do so without getting the basics. There's no any other forum that offers such a comfortable environment to ask questions. I would be dissapointed if I don't get answers. So, please help me.

With aids from Wikipedia, Microsoft Encarta and above all, Physics Forums, I have summarized what I got. So, correct me if I am wrong.

1: Potential : The electric potential energy at a point is equal to the electric potential energy of a charged particle at that location divided by charge of the particle.

My question is : What is "Electric Potential Energy" and on what factors does it depend ?

2) Voltage : For voltage, I have got a really nice definition from Encarta. The more willing the terminals are to give up and receive electrons, the higher the voltage.

What I have found is I understand things when they are in free space but problem begins with wires and batteries.

 

[Studiot]

1: Potential : The electric potential energy at a point is equal to the electric potential energy of a charged particle at that location divided by charge of the particle.

And how does a charged particle come by this electric potential energy?

It takes two to tango.

You need at least two charges in the system for there to be any electric potential.

 

[Naty1]

More insights in this discussion:

https://www.physicsforums.com/showthread.php?t=565244&highlight=voltage

 

[rcgldr]

It would probably be easier to explain electrical potential and voltage related to points in a constant electrical field, such as between the plates of a very lage cacpacitor with opposite but equal magnitude charges on each plate.

The convention for electrical potential (voltage) is based on a postive charge within the field so the direction of the field is from the positive plate towards the negative plate. The minimum voltage corresponds to the surface of the negative plate, and the maximum voltage corresponds to the surface of the positive plate. The voltage difference between two points in a constant electrical field equals the force per unit charge times distance (relative to the plates) between the two points, and can be expressed as Newton (force) x meters (distance) / coulomb (unit of charge). For a current, the unit of charge would be 1 amp second, so for current, 1 volt = 1 (Newton meter) / (amp second).

If you consider the electrical potential energy of a positively charged object, it's greatest at the surface of the positive plate and lowest at the negative plate (EPE would be exchanged for KE if the positively charged particle were allowed to accelerate towards the negative plate, free of any other forces (like aerodynamic drag)). A negatively charge particle would reverse the sign of the electrical potential energy (it would be greatest (most positive) at the negative plate).

 

[sophiecentaur]

.

You need at least two charges in the system for there to be any electric potential.

This is not correct. The Potential is defined as the Energy that would be transferred when a fictional Unit Charge is moved to that point in a field. You only need one charge to set up a field. The 'probe' charge doesn't have to exist for the potential to exist, any more than a planet has to exist for the Sun's gravitational potential to be what it is at a point in space.

 

[Studiot]

This is not correct. The Potential is defined as the Energy that would be transferred when a fictional Unit Charge is moved to that point in a field. You only need one charge to set up a field. The 'probe' charge doesn't have to exist for the potential to exist, any more than a planet has to exist for the Sun's gravitational potential to be what it is at a point in space.

This is playing with words. Both the gravitational and electric potentials are as real or as fictional as the test particles.

 

[sankalpmittal]

This is playing with words. Both the gravitational and electric potentials are as real or as fictional as the test particles.

No Studiot, sophiecentaur is correct. Electric potential is the amount of work done in moving a charge from infinity to a particular point. Its the energy transferred in moving that charge to a particular point. Its not any kind of difference where you need two charge systems. In other words if 1 coulomb charge is being moved upto distance of x metres of wire then the energy manifested is electric potential. Think about why we use infinity in the above definition of electric potential. That's what make potential difference "different" from electric potential.

Electric potential = Sum total of potential differences up to that point.
Electric potential = V_n-V₀
Where V₀ = 0 at starting
So
Electric potential = V_n

While potential difference at two points = V₂-V₁

We have to use correct terminologies at correct place if we are explaining to somebody.

 

[sophiecentaur]

This is playing with words. Both the gravitational and electric potentials are as real or as fictional as the test particles.

I am not just playing with words. The field is something that needs to be considered on its own. You are right in saying that the force between two charged particles 'needs' each particle to be there but how would you use that approach to describe what happens when a Radio wave produces currents in a wire or where low frequency radio waves actually cause electrons to move about in the Ionosphere? There is no 'second charge', in those cases, for the electrons to "tango" with. It is absolutely necessary to involve fields (/potential) in those cases, which don't relate in any way to other charges.

In this thread, we are discussing Potential in a circuit or somewhere in space and you might say it's all to do with zillions of electrons affecting each other. But you would need to calculate all the individual interactions if you treated it on a charge-to-charge basis. (I read earlier of "electrons bumping into each other). It makes far more sense to consider each charge, on its own, in an overall Potential situation.

 

[Studiot]

No Studiot, ...etc

How you you reconcile this with Coulomb's Law?

This law is the fundamental law of electrical science at this level.

Actually SophieCentaur identifies two charges, he just says that one is 'ficticious' and implies that it therefore doesn't count in the reckoning.

 

[sophiecentaur]

How you you reconcile this with Coulomb's Law?

Why would you claim that any reconciliation is needed? Coulombs law discusses the Potential due to the existence of two charges. It doesn't say that is the only way to treat Fields. You can rearrange Coulomb's law and substitute some of the terms with E without any conflicts. The integral of E over distance will tell you the Potential in all circumstances.