Electromagnetism !

This is a bad habit. Generally the direction current is all that matters, and not the polarity of the charge carriers. The instances where the polarity of the charge carriers is important are very few and far between (e.g. the Hall effect). Unless you are working with one of those you will be better off simply thinking about the direction of the current.

This is not generally true. There are circumstances where the charge carriers are positive. E.g. proton beams. There are even cases where the charge carriers are both positive and negative. E.g. electrolytes. In particular, when you have both positive and negative charge carriers trying to think in terms of both ion flows will lead to nothing but confusion.

This is wrong. Current can easily be negative. As ZapperZ mentioned above, the quantity that is actually of interest for physics is not current, but current density, which is a vector. When you go from current density to current you have to specify a surface and a surface normal, at least implicitly. Once you do so, a current going one way across the surface is positive and a current going the other way across the surface is negative.
http://en.wikipedia.org/wiki/Current_density#Current_through_a_surface

You can have a current of both and charges do move.

They either have to go from north to south or from south to north. We just picked a convention and used it. It is just a convention, use it consistently and you will get the right answer for any measurement you choose.

Hello DaleSpam,
This is not the bad manner but just the healthy contradiction. How can charges move ? In proton accelerators we move a proton which is just a subatomic particle having +1 charge.
So the particle is moving and not the charges I think.

You said:

... I was hoping you'd link the magnetic field from electric currents with the magnetic field from a bar magnet. How would does the arrangement of electrons relate to an electric current?

In the planetary model of the atom - electrons orbit the nucleus in a circle[*]. An electron moving in a circle is an electric current in a loop (see pic below) - so we would expect atoms to have a magnetic field the same way a current loop does. In a solid object, the atom's magnetic fields are randomly arranged, so they mostly cancel each other out and what's left is too small to notice. In a permanent magnet, enough atomic magnetic fields are oriented the same way to be noticed.

I kinda like this example because it illustrates how connected everything gets when you look carefully.

Note: we often use magnitudes of vectors in calculations - for convenience. eg. gravitational force and acceleration are usually quoted as scalars even though they are vectors ... the direction is taken from context.

When we talk about current in a DC electric circuit, the direction of the current almost always makes no difference to the results of our calculations while making the actual math harder so we leave it off. However, if you look at circuit analysis - like Kirkoffs Laws - you will see current is always drawn as an arrow (vector). In AC circuits, the current and voltage are described as a rotating vector called a phasor.

Because it can make a difference, we need to remember this and adjust what we do when it becomes important. Usually we can get the direction from the context when this happens. In the equation you use an an example, the only part of the current that is affected is the magnitude. The direction is implied.

Basically, we don't like to do more math than we have to.

[URL]http://www.physics.sjsu.edu/becker/physics51/images/29_22_Magnetic_dipole_moment.JPG[/URL]
-- -- stolen from: PHYSICS 51 notes San Jose University.
The $\bf \mu$ is the direction of the north pole and is called the "magnetic moment". The $\bf L$ is the moment of inertia of the electron.

----------------------

[*] The actual situation is more subtle than that - but atoms still have their own magnetic fields - called "magnetic moments" - which come from the symmetries in the electrons.

Hmm little sophisticated to grasp but its a bit satisfying.

Here was my complete answer (quoted) :
The answer is but the Earth's magnetic field. It flows from south pole to the north pole. When it links itself (magnetic flux) with a permanent magnet , it induces opposite poles in permanent magnet in which magnetic lines of forces flow from north pole to south pole. This is due to the process mutual magnetic induction.

Now the question arises that if we keep an iron bar will it behave as a magnet ? No ! We must convert it to a magnet : Single touch method , divided touch method , double touch method or electrical method. If we follow either of methods electrons come in pairs in straight lines having net electrostatic force. This is Ewing's molecular theory of magnetism.

e- e- e- e- e- e- e-
e- e- e- e- e- e- e- --> Like this in a permanent bar magnet.

Like this in normal iron bar :

e- e-
e-
e- e- e-

Its correct , according to you ? Right ? Yes I know that in magnets electrons form straight line giving rise to net force attraction. In iron bars , the electrons in random pattern mutually cancel each others force of attraction , giving rise to zero net force. I could even more elaborate but my hand would ache very badly so I thought it might me better to be brief here.

:)
Thanks again.

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Dale
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How can charges move ? In proton accelerators we move a proton which is just a subatomic particle having +1 charge. So the particle is moving and not the charges I think.
The word "charges" is short hand for "charged particles". Note the difference between "charge" which refers to the property of the particle and "a charge" or "charges" which refer to one or more charged particles respectively.

In any case this distinction is rather meaningless, particles move and charge is a property of the particle. The charge associated with a particle is here now and there later. Therefore charge moves, regardless of if you say "charge", "a charge", or "charges".

By the way, this is a very minor point compared to the rest of the big errors that you made. You should look into the remainder of my post and reconsider your many incorrect statements.

Simon Bridge
Homework Helper
Here was my complete answer (quoted) :
[snip]

Its correct , according to you ? Right ?
No.
Yes I know that in magnets electrons form straight line giving rise to net force attraction.
No they don't. In order to make a magnetic field, the electrons have to be moving.[/quote]

BTW: you don't have to quote the entire passage - the original has not gone anywhere. Just the bit that you are replying to is good enough.

The word "charges" is short hand for "charged particles". Note the difference between "charge" which refers to the property of the particle and "a charge" or "charges" which refer to one or more charged particles respectively.

In any case this distinction is rather meaningless, particles move and charge is a property of the particle. The charge associated with a particle is here now and there later. Therefore charge moves, regardless of if you say "charge", "a charge", or "charges".

By the way, this is a very minor point compared to the rest of the big errors that you made. You should look into the remainder of my post and reconsider your many incorrect statements.

Ok , so in this case , I referred to "charge" and not "charges" . "Charge" just can't move as it is a property and not a particle. You must be referring to "a test charge" which is moved in an electric circuit by the application of potential difference. I reconsidered my flaws.

V2-V1 = W/Q

No.
No they don't. In order to make a magnetic field, the electrons have to be moving.

BTW: you don't have to quote the entire passage - the original has not gone anywhere. Just the bit that you are replying to is good enough.

Do you mean centrifugal force of valence electrons in the last shell of an atom ?
Electrons don't orbit the nucleus. Heinsberg uncertainity principle tells that you just can't be sure of. Orbital is the correct term. The probability says that most electrons are found in orbitals. Yes , I reread your post.

Here is Ewing's Molecular theory of magnetism :
http://www.winnerscience.com/magnetic-materials-2/molecular-theory-of-magnetism/
http://sciencemagicnew1.blogspot.com/2009/11/ewings-molecular-theory-of-magnetism.html (images are bit vague).

Dale
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"Charge" just can't move as it is a property and not a particle.
It is here now and there later, therefore it moves. QED

Do you understand why current can be negative and why it is usually best to consider conventional current regardless of the polarity of the charge carriers?

Simon Bridge
Homework Helper
Do you mean centrifugal force of valence electrons in the last shell of an atom ?
No. I said magnetic moment and I meant it. Centrifugal force is a different thing all together.

Electrons don't orbit the nucleus. Heinsberg uncertainity principle tells that you just can't be sure of. Orbital is the correct term. The probability says that most electrons are found in orbitals. Yes , I reread your post.
Then you also read the bit where I said it is actually more subtle than the planetary model would imply.

The orbital refers to an energy eigenstate, which may be shared by two electrons. Orbitals have a magnetic moment which contribute to an overall atomic magnetic moment.

Here is Ewing's Molecular theory of magnetism :
I'm very familiar with it. You realize this model comes from the 19th century right?

In Contributions to the Molecular Theory of Induced Magnetism[1], Ewing et al point to Ampere (who was developing the idea about atomic magnetic moments) to explain how the molecules become magnetic in the first place. His theory is intended to account for the way bulk materials may become magnetized by tapping or what-have-you.

Anyway - where does Ewing talk about electrons lining up? Ewing talks about each molecule of a solid being a magnet, and that magnetized materials have these molecular magnets all lined up. These days we talk about magnetic domains for the same thing.

So - can you now relate Ewing theory to Ampere's law?

---------------------------

[1] Published in Proceeding of the Royal Society of London 1890 and retrieved from the JSTOR archives.

It is here now and there later, therefore it moves. QED

Do you understand why current can be negative and why it is usually best to consider conventional current regardless of the polarity of the charge carriers?

Hello DaleSpam,

What ? Charge is here now and there later ? Do you think this statement can solve my problem ? My question is that simple : How can charge (be it positive or negative) move along an electric circuit ? Current can be negative , yes but it is just meaningless to consider direction in DC circuits , right ? My question is just regarding an electric circuit. However calculations won't be affected if we change the polarities of current flow.

The truth is out there I think : http://www.apex.net.au/~pet/jf31.html . See the last sentence in caps lock.

No. I said magnetic moment and I meant it. Centrifugal force is a different thing all together.

Then you also read the bit where I said it is actually more subtle than the planetary model would imply.

The orbital refers to an energy eigenstate, which may be shared by two electrons. Orbitals have a magnetic moment which contribute to an overall atomic magnetic moment.

I'm very familiar with it. You realize this model comes from the 19th century right?

Anyway - where does Ewing talk about electrons lining up? Ewing talks about each molecule of a solid being a magnet, and that magnetized materials have these molecular magnets all lined up. These days we talk about magnetic domains for the same thing.

So - can you now relate Ewing theory to Ampere's law?
Hello Sir Simon,

Ewing never talked about electrons lining up. He stated : Every smallest of the smallest substance itself behaves as a magnet if the molecules line up in a straight line giving rise to a net magnetic force.
Code:
→ → → → → → →
→ → → → → → →
→ → → → → → →

In an unmagnetized substance molecules are in haphazard or random manner and hence their magnetic force mutually cancels each others.
Code:
→           |
|     →
\      →   \

_____________________________________________________________________

But this led to an idea that even an electron can act as a dipole or a free magnet. A metal has large number of free electrons which move on a metal surface in any direction but does not leave the metal surface itself. Hence there is no net flow of electrons in any particular direction. But when we apply potential difference at any two points , there is net flow of electrons. We are talking about electromagnetism so potential difference (electromotive force) is created by electromagnetic induction. These electrons even spin about their own axis which is known as their magnetic moment which is tangential.

Relation between Ewing theory to Ampere's law?
Well Ampere's law states that in a section of a wire magnetic field produced will be of course on a plane at right angle to the direction of flow of current and its intensity is tangential. This magnetic field is given by ,
B= μ0 I/2πr
where μ0 is magnetic constant , I is current flow and 2πr is circumference of circle in magnetic field.

This is all I know about Ampere's law. Ewing's theory tell you about each molecule being lined up so ......

I am after all , still in class 10th , 14 years.

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Dale
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My question is that simple : How can charge (be it positive or negative) move along an electric circuit ? Current can be negative , yes but it is just meaningless to consider direction in DC circuits , right ?
No, it is most definitely not meaningless to consider the direction of current in a DC circuit. If you get the direction wrong then you will incorrectly show resistors mysteriously providing energy and batteries somehow dissipating energy. Energy won't be conserved locally. You will also get the polarity of an electromagnet backwards. The direction of current is always important, even in DC applications.

My question is just regarding an electric circuit. However calculations won't be affected if we change the polarities of current flow.
Having done such calculations for many years I can tell you without reservation that many calculations will be wrong if you incorrectly change the polarity of the current.

The truth is out there I think : http://www.apex.net.au/~pet/jf31.html . See the last sentence in caps lock.
Oh, wow, somebody on the internet disagrees with me and they used all caps! That must mean that I am wrong, nobody would ever put anything incorrect in all caps.

I am after all , still in class 10th , 14 years.
I am very impressed with your advanced knowledge for your age. But as advanced as you are for your age, you may want to re-think the wisdom of disagreeing with people who have been doing circuits for significantly longer than you have been alive. Current goes in the opposite direction as the motion of the electrons, i.e. from the positive terminal of a battery through the circuit back to the negative terminal. Trying to identify the direction of the current with the direction of the charge carriers will lead to lots of mistakes and needless confusion.

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Simon Bridge
Homework Helper
No, it is most definitely not meaningless to consider the direction of current in a DC circuit. If you get the direction wrong then you will incorrectly show resistors mysteriously providing energy and batteries somehow dissipating energy. Energy won't be conserved locally. You will also get the polarity of an electromagnet backwards. The direction of current is always important, even in DC applications.
Technically, if one decided to change the convention for current in a circuit, many other rules will have to change sign too. For instance, the rule for the polarity of an electromagnet would be a left-hand one (or you put the arrows on the letters pointing the other way).

That said - it is useful to have a conventional current - a lot of the math gets simpler, not having to worry about two cases.

If I really need to deal with the physical current I can deal with the charge flux as something like the conventional current multiplied by the charge ... since electrons are negative, that reverses the direction of the vector while keeping the positive flux consistent with the definition of the electric field direction (recall - it is the direction that a positive charge moves off in).

I think there was some confusion over my comments about why we do not always explicitly write current as a vector ... the reason is because it is not always convenient to do so. In an electric circuit, the direction of the current is supplied by context - just look to the phase of the voltage or current source in the circuit.

However, when you analyse a circuit with kirkoffs laws, for eg, you have to make the current directions explicit everywhere.

It's really annoying to have to stand on authority to make someone pay attention! One of my professors held the Dirac prize, and I, as a lowly grad student, was able to disagree with him quite successfully in the field in which he was awarded. I was surprised to be taken seriously, and not once did he stand on his authority and experience which was vastly greater than my own.

Unfortunately there is a difference between being right and being persuasive.

Bottom line is - in this case - the convention exists and OP will just have to learn to live with it. It doesn't matter if he believes there is a good reason for it or if the imps of history chose it just to make his life difficult - it is a fact of life get over it. End of story.

Dale
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For instance, the rule for the polarity of an electromagnet would be a left-hand one (or you put the arrows on the letters pointing the other way).
You are right, and it would be even more complicated than that in many circumstances. For instance, in electrolytes you would have both left handed fields from the negative charge carriers and simultaneously you would have right handed fields from the positive charge carriers. This is important for pacemakers, neuro-prosthetics, transcranial magnetic stimulation, and magnetoencephalography. You would run into similar problems studying plasmas like the sun.

It would be a simple change of convention to make electrons be positively charged. But regardless of your convention for the charge of an electron, it is important that current point in the opposite direction of the motion of negative charge carriers. Keeping in mind that despite the fact that electrons are the charge carriers in metal there are always going to be some circumstances where protons are charge carriers that you need to deal with also.

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Simon Bridge
Homework Helper
Yeah - if you wanted to have a different current direction for each charge. And what was the expected gain again? It may not confuse students as much? Wasn't that it?

You are right, and it would be even more complicated than that in many circumstances. For instance, in electrolytes you would have both left handed fields from the negative charge carriers and simultaneously you would have right handed fields from the positive charge carriers. This is important for pacemakers, neuro-prosthetics, transcranial magnetic stimulation, and magnetoencephalography. You would run into similar problems studying plasmas like the sun.

It would be a simple change of convention to make electrons be positively charged. But regardless of your convention for the charge of an electron, it is important that current point in the opposite direction of the motion of negative charge carriers. Keeping in mind that despite the fact that electrons are the charge carriers in metal there are always going to be some circumstances where protons are charge carriers that you need to deal with also.

Yeah - if you wanted to have a different current direction for each charge. And what was the expected gain again? It may not confuse students as much? Wasn't that it?

Not sure what people mean by charge flow in electric circuits ?
Here are certain sites which point out that current flow from positive to negative in reality in DC. Can you grasp little bit of it ? I find it quite sophisticated. How can charge flow in an electric circuit ? Please tell.

I find excellent bunch of sites which claim that current flows from positive to negative due to back attraction. In other words , it agrees with DaleSpam.

1. http://amasci.com/amateur/elecdir.html
2. http://www.asmcommunity.net/board/index.php?topic=12847.0
4. http://amasci.com/miscon/eleca.html#frkel

Originally quoted by www.amasci.com/miscon/eleca.html#frkel :

I try to take my own advice: I always imagine that electric currents in circuits are not flows of electrons, instead they are flows of "charges" or "charged particles." Unless we know what kind of conductor is involved, we cannot know whether an electric current is composed of moving electrons... or whether it's electrons AND positive atoms moving, or whether it's moving positive and negative atoms. For example, if you receive an electric shock, no electrons flowed through your body. Only charged atoms flowed.

This vividly agrees with DaleSpam.

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We all remember the old TVs with the giant "cathode ray" picture tube. (I even remember and experimented with "vacuum tubes" when I was a kid). In them, electrons streamed from a heated negatively charged electrode and were accelerated by an electric field to paint a picture on the front screen. There was no "back flow" of positive charges in these devices. If there were, the picture producing surface would disappear pretty quickly.

Certainly, one could posit that as a stream of electrons drift through a wire, there could be a series of (+) holes drifting in the other direction. If we did, we would have to be careful not to get trapped by saying for example, that in a wire we have a + current of 2 amps flowing left and a - current of 2 amps flowing right. It is one or the other. I guess this is obvious so why don't we all just call it a day and "go with the flow".

Simon Bridge
Homework Helper
In semi-conductors we talk about "charge carriers" too - there are lots of approximations and shorthands in electrophysics.

Here are certain sites which point out that current flow from positive to negative in reality in DC.
Well if it is on the internet it must be true.
Can you grasp little bit of it ? I find it quite sophisticated. How can charge flow in an electric circuit ? Please tell.
Positive charges flow in the direction of the electric field - negative charges the opposite. What's the problem?

In semi-conductors we talk about "charge carriers" too - there are lots of approximations and shorthands in electrophysics.

Well if it is on the internet it must be true.
Positive charges flow in the direction of the electric field - negative charges the opposite. What's the problem?

I am talking of an electrical DC circuit of metal wires :

1. Which way is current really flowing (i.e. in reality) ?

2. What is current ? Rate of flow of charges (positive charges or negative charges ?) or Rate of flow of electrons ?

3. How are charges really drifting in metal wires circuits ? What actually drifts electrons or charges ?

4. Charge is a property and electrons are subatomic particle , right ? Then how can a property drift ? Are not these electrons ?

5. What is charge really if we talk in this aspect ?

6. Is this analogy correct -: THE CURRENT ALWAYS MOVE FROM NEGATIVE TO POSITIVE.
A 'conventional current flow' does not exist. It is like saying steam is going into the boiling water in the kettle and becomes water. It simply is not so.

7. Are electrons carrying negative charge with them what you call charge flow ? How can positive charge move then ?

_____________________________________________________________________

In the sites I posted the analogy given was that
Code:
e[SUP]-[/SUP]     +         e[SUP]-[/SUP]         +    e[SUP]-[/SUP]        +            e[SUP]-[/SUP]            +               e[SUP]-[/SUP]     +        e[SUP]-[/SUP]
------------------------------------------------------------------------------------------------->

---> shows direction of electron. In that site it was given that as electrons drift and change location positive charges develop in metal atoms which is responsible in electric current and not electrons. Is this true ?

Answer these questions and I'll be relieved.
:)

Dale
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Not sure what people mean by charge flow in electric circuits ?
Here are certain sites which point out that current flow from positive to negative in reality in DC. Can you grasp little bit of it ? I find it quite sophisticated. How can charge flow in an electric circuit ? Please tell.
Consider some position in the circuit. Imagine a plane cutting across the wire at that location, and pick a direction (e.g. right) to be positive. Start a clock and every time a + charge goes across to the right or a - charge goes across to the left you will increase a counter, and every time a + charge goes across to the left or a - charge goes across to the right you will decrease the counter. Stop your clock and your count. Multiply your count by the electron charge and divide it by the time on your clock. That is current.

Dale
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1. Which way is current really flowing (i.e. in reality) ?
Current is really flowing in the opposite direction that electrons are drifting.

2. What is current ? Rate of flow of charges (positive charges or negative charges ?) or Rate of flow of electrons ?
See my response to your previous post.

3. How are charges really drifting in metal wires circuits ? What actually drifts electrons or charges ?
Electrons, which are negative charge carriers.

4. Charge is a property and electrons are subatomic particle , right ? Then how can a property drift ? Are not these electrons ?
Because it is carried by the charge carriers (electrons in metal) which drift.

5. What is charge really if we talk in this aspect ?
Charge is a property of fundamental particles which describes their interaction with the electromagnetic force (photons).

6. Is this analogy correct -: THE CURRENT ALWAYS MOVE FROM NEGATIVE TO POSITIVE.
A 'conventional current flow' does not exist. It is like saying steam is going into the boiling water in the kettle and becomes water. It simply is not so.
No. Current goes from positive to negative. Current is defined to go in the opposite direction as electrons or other negatively charged charge carriers.

7. Are electrons carrying negative charge with them what you call charge flow ? How can positive charge move then ?
In metals the positive charge carriers are tightly bound and don't move much (very small thermal motions). However, in other types of materials, such as electrolytes and plasmas, the positive charges are not tightly bound and can also move.

Consider some position in the circuit.

Ok.
Imagine a plane cutting across the wire at that location, and pick a direction (e.g. right) to be positive.

You mean a plane perpendicular to wire at a point ? If so then okay .

Start a clock and every time a + charge goes across to the right or a - charge goes across to the left you will increase a counter, and every time a + charge goes across to the left or a - charge goes across to the right you will decrease the counter.

How are positive charges moving ? [PLAIN]http://www.cci-compeng.com/Unit_2_Electronics/Unit_2_Images/2102_Current.gif [Broken]

In image the electrons are drifting in a particular direction. Every time the atoms in wire loose electrons from their last orbit , and jump into another atom , they develop positive charge in atom behind them which stays in its position and doesn't move. In image those numbers like 1 , 2, 3 , 4 are the number of positive charges. Electrons move and they develop those positive charges. In fact due to loss of electrons.

I can only understand - what you mean is that if electrons go across the left , i.e. negative charge carriers then there is loss of electrons so I must increase the counter.

Aren't positive charge developed in metal atoms due to loss of electrons are fixed and not moving ? How can they move ?

Stop your clock and your count. Multiply your count by the electron charge and divide it by the time on your clock. That is current.
Ok.

Current is really flowing in the opposite direction that electrons are drifting.
Ok , so is this the discharge or kind of force between positive charges and electrons ?
See my response to your previous post.
You mean that current is the rate of flow of charges.

Electrons, which are negative charge carriers.
Ok.
Because it is carried by the charge carriers (electrons in metal) which drift.
Ok.
Charge is a property of fundamental particles which describes their interaction with the electromagnetic force (photons).

No. Current goes from positive to negative. Current is defined to go in the opposite direction as electrons or other negatively charged charge carriers.

In metals the positive charge carriers are tightly bound and don't move much (very small thermal motions). However, in other types of materials, such as electrolytes and plasmas, the positive charges are not tightly bound and can also move.

Ok.
Code:
e-     +         e-         +    e-        +            e-            +               e-     +        e-
------------------------------------------------------------------------------------------------->
---> shows direction of electron. In that site it was given that as electrons drift and leave behind positive charges due to their loss which are developed in metal atoms which is responsible in electric current and not electrons. Is this true ?

:)

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Dale
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You mean a plane perpendicular to wire at a point ? If so then okay .
If you are familiar with the vector normal to a plane and the dot product you can extend it to arbitrary shaped surfaces, but a plane is fine.

How are positive charges moving ?
1) I was providing a general definition which would work in the case of positive charge carriers also
2) There is always some thermal motion of the lattice, so on a microscopic scale even in metal you will get positive charges vibrating back and forth across your plane. This thermal motion averages out to 0 and does not contribute to the current, but if you are counting each charge crossing your plane it will have to be considered.

Ok , so is this the discharge or kind of force between positive charges and electrons ?
Current is the movement or flux of charge, it doesn't have units of force.

In that site it was given that as electrons drift and leave behind positive charges due to their loss which are developed in metal atoms which is responsible in electric current and not electrons. Is this true ?
The electrons are the charge carriers in metal. Their drift is responsible for current, and current is defined (see above) in such a way that it points in the direction opposite the drift of the electrons.

If you are familiar with the vector normal to a plane and the dot product you can extend it to arbitrary shaped surfaces, but a plane is fine.
Ok , if that is fine really. :)
1) I was providing a general definition which would work in the case of positive charge carriers also
2) There is always some thermal motion of the lattice, so on a microscopic scale even in metal you will get positive charges vibrating back and forth across your plane. This thermal motion averages out to 0 and does not contribute to the current, but if you are counting each charge crossing your plane it will have to be considered.

Ahh I see !
Now I imagine the real idea of current flow. It is because of the positive charge in metal atoms and electrons or negative charge carriers only contribute to it ! Even that small vibrant motion of positive charged ions is to be considered here.

This means Benjamin Franklin was correct ! Current is the rate of flow of charges and not electrons even in metal wires.

Current is the movement or flux of charge, it doesn't have units of force.

Actually I wanted to mean something else and I typed something else !
Sorry for my grammatical error. I meant that current is the flux which is produced due to back attraction force of electrons and positive charges in metal atoms.

I think I am correct and this is what you mean that current hence flows opposite to flow of electrons in most of cases in metals even.

The electrons are the charge carriers in metal. Their drift is responsible for current, and current is defined (see above) in such a way that it points in the direction opposite the drift of the electrons.

Ok I get it now !

Thank you very much !

Dale
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I meant that current is the flux which is produced due to back attraction force of electrons and positive charges in metal atoms.
Yes, this is basically a re-statement of Ohm's law, which applies in metals as long as they are not superconductive.

Ok I get it now !
Excellent! I am glad to hear it.