I am trying to understand voltage

[nm825]

So, I know voltage is work per charge. More basically, I know you can think of voltage of how bad a charge (let's say an electron) wants to move from one point to another. So, let's say we have an electron at a negative terminal; it's potential is going to be higher than if it was at the positive terminal. Because we are always trying to go from high energy to low energy, the electrons will migrate to the positive terminal, if the two terminal are connected by conductive wire, and current will flow from positive to negative.


Is my intuition right on this stuff?

---

Members don't see this ad.

 

[gettheleadout]

The analogy here might be of help: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html

But yes, your intuition is correct so far.

 

[sps27]

So, I know voltage is work per charge. More basically, I know you can think of voltage of how bad a charge (let's say an electron) wants to move from one point to another. So, let's say we have an electron at a negative terminal; it's potential is going to be higher than if it was at the positive terminal. Because we are always trying to go from high energy to low energy, the electrons will migrate to the positive terminal, if the two terminal are connected by conductive wire, and current will flow from positive to negative.


Is my intuition right on this stuff?

That is a good question, and I must say Kaplan does a great job in explaining concepts like this. There are two concepts related to one another, Electrical Potential Energy and Electrical Potential.

1) When one charge q is separated from another charge Q, the charges will have an electrical potential energy due to their proximity .with one another, given by U = kqQ/r. If the charges are like charges, the potential energy is +ve and if they are unlike, the potential energy is -ve.

Consider two charges, a stationary -ve source charge and a +ve test charge that can be moved. Opposite charges will have -ve potential energy and this energy will become increasingly -ve as the charges are brought closer and closer together. Don't be confused by the -ve sign on potential energy; increasingly -ve numbers are actually decreasing, because they are moving farther away from 0.

Now Consider two +ve charges. As like charges, these will exert repulsive forces and the potential energy of the system will be positive. Since like charges repel each other, the closer they are to each other, the unhappier they are, so in this case, the like charges will become more stable the further apart they move.

The basic concept is 'when like charges are moved towards each other, the electric potential energy of the system increases; when like charges move apart, the electric potential energy of the system decreases. When unlike charges move towards each other, the electric potential energy of the system decreases; when unlike charges are moved apart, the electric potential energy of the system increases. This is the basic concept. If allowed, a charge will move in whatever direction results in the decrease of the system's electric potential energy.


2) Electrical potential is defined very simply as the ratio of the charge's electrical potential energy to the charge itself i.e. U/q. In other words it is the electrical potential energy to move a unit charge.

When a +ve charge moves spontaneously through an electrical field, it will move from a position of higher electric potential (higher electrical potential energy / charge) to a position of lower electrical potential (lower electrical potential energy / charge). Positive charges move spontaneously from higher voltage to low voltage.

And now the most important thing to understand comes now.

When a -ve charge moves spontaneously through an electric field, it will move from a position of lower electrical potential (higher electric potential energy /-ve charge) in other words, low voltage, to a position of higher electric potential (lower electric potential energy /-ve charge), in other words, high voltage. Negative charges move spontaneously from low voltage to high voltage..

Current is defined as movement of +ve charge and is in the direction of + higher voltage to - lower voltage end of a battery. In a circuit the charges actually moving are the -ve charged electrons, which move from low voltage end to a higher voltage end.

The above information is straight from Kaplan Physics book page 174~177, not the whole, just bits and pieces that I think are important to understand.

And this is my own understanding.

3) By Definition the source charge is considered +Q and a unit test charge is considered +ve. The confusion most people have I think is due to definition of Electric potential energy which is defined as the amount of work necessary to bring a unit test charge from infinity to that region or point in space. The reason infinity is chosen is because in the eqn for electrical potential energy, if we substitute infinity for r, we get 0. So infinity is considered as 0 potential or state of lowest electrical potential energy for a +ve charge.

So if I bring a unit +ve charge q from infinity towards +Q(source charge), I will be increasing the electric potential energy of the charge q which will become more and more because the charges will repel and are unhappy about this movement. Think of this as a movement on the +ve x axis and away from 0 i.e., increasingly +ve and more.

On the flip side if I take a unit -ve charge at infinity the electric potential energy of that charge is -0. If I move that charge towards +Q, it likes that movement because unlike charges attract and so the electrical potential energy of the charge decreases. Think of this as a movement on the -ve x-axis and away from 0 i.e., lesser and lesser. In other words, the 0 or infinity represents the state of highest electrical potential energy for a -ve charge.

So this is the basic concept - I think. Off course, I could be wrong so let me know if any of this is incorrect.

 

[ND13]

Spot on. Your explaination helped me understand it a lot better than what Kaplan did.

Except for the last point. taking a -ve charge from infinity, the electric potential energy would not be -0 (it would be infinity). As it moves towards the +Q it reaches 0.

Everything else though, top notch.

That is a good question, and I must say Kaplan does a great job in explaining concepts like this. There are two concepts related to one another, Electrical Potential Energy and Electrical Potential.

1) When one charge q is separated from another charge Q, the charges will have an electrical potential energy due to their proximity .with one another, given by U = kqQ/r. If the charges are like charges, the potential energy is +ve and if they are unlike, the potential energy is -ve.

Consider two charges, a stationary -ve source charge and a +ve test charge that can be moved. Opposite charges will have -ve potential energy and this energy will become increasingly -ve as the charges are brought closer and closer together. Don't be confused by the -ve sign on potential energy; increasingly -ve numbers are actually decreasing, because they are moving farther away from 0.

Now Consider two +ve charges. As like charges, these will exert repulsive forces and the potential energy of the system will be positive. Since like charges repel each other, the closer they are to each other, the unhappier they are, so in this case, the like charges will become more stable the further apart they move.

The basic concept is 'when like charges are moved towards each other, the electric potential energy of the system increases; when like charges move apart, the electric potential energy of the system decreases. When unlike charges move towards each other, the electric potential energy of the system decreases; when unlike charges are moved apart, the electric potential energy of the system increases. This is the basic concept. If allowed, a charge will move in whatever direction results in the decrease of the system's electric potential energy.


2) Electrical potential is defined very simply as the ratio of the charge's electrical potential energy to the charge itself i.e. U/q. In other words it is the electrical potential energy to move a unit charge.

When a +ve charge moves spontaneously through an electrical field, it will move from a position of higher electric potential (higher electrical potential energy / charge) to a position of lower electrical potential (lower electrical potential energy / charge). Positive charges move spontaneously from higher voltage to low voltage.

And now the most important thing to understand comes now.

When a -ve charge moves spontaneously through an electric field, it will move from a position of lower electrical potential (higher electric potential energy /-ve charge) in other words, low voltage, to a position of higher electric potential (lower electric potential energy /-ve charge), in other words, high voltage. Negative charges move spontaneously from low voltage to high voltage..

Current is defined as movement of +ve charge and is in the direction of + higher voltage to - lower voltage end of a battery. In a circuit the charges actually moving are the -ve charged electrons, which move from low voltage end to a higher voltage end.

The above information is straight from Kaplan Physics book page 174~177, not the whole, just bits and pieces that I think are important to understand.

And this is my own understanding.

3) By Definition the source charge is considered +Q and a unit test charge is considered +ve. The confusion most people have I think is due to definition of Electric potential energy which is defined as the amount of work necessary to bring a unit test charge from infinity to that region or point in space. The reason infinity is chosen is because in the eqn for electrical potential energy, if we substitute infinity for r, we get 0. So infinity is considered as 0 potential or state of lowest electrical potential energy for a +ve charge.

So if I bring a unit +ve charge q from infinity towards +Q(source charge), I will be increasing the electric potential energy of the charge q which will become more and more because the charges will repel and are unhappy about this movement. Think of this as a movement on the +ve x axis and away from 0 i.e., increasingly +ve and more.

On the flip side if I take a unit -ve charge at infinity the electric potential energy of that charge is -0. If I move that charge towards +Q, it likes that movement because unlike charges attract and so the electrical potential energy of the charge decreases. Think of this as a movement on the -ve x-axis and away from 0 i.e., lesser and lesser. In other words, the 0 or infinity represents the state of highest electrical potential energy for a -ve charge.

So this is the basic concept - I think. Off course, I could be wrong so let me know if any of this is incorrect.

 

[desperadoflakes]

Great explanation. The ideas that really helped me understand were:

-To talk about electric fields, we think of a simple system in space in which there is a large positive "source charge", which we refer to as Q, and a small positive "test charge", which we refer to as q. In our imaginary system, the force between Q and q is given by Coulomb's law.

-The electric field is the force given by coulomb's law, applied to "q" at a given point in space. To draw an electric field, we can put q in a bunch of different spots, and measure the direction and magnitude of the force it feels. The electric field tells us the direction the charge will go, and the strength with which it will get pushed. Because we define the electric field as the force being produced by Q (and not by q), we define our electric field as E = F/q. We rearrange this to give F = E * q

-The electrical potential energy U is defined as the total energy (work) required to move q against the electric field. Because work = F * d, U = E * q * d
Imagine yourself physically pinching q, and dragging it towards Q. Because they are like charges, and because E gets stronger as you get closer to Q, it will become increasingly difficult to drag it close. This shows that q is building up potential energy. When you let it go, it will fly away! That's the potential energy being released as kinetic energy.

-If we measure the potential energy of q when held very close to Q, U will be very high. If we measure potential energy when q is far from Q, U will be very low.
When we defined E, we noted that the force that q feels at any point is due to Q. Now, when we define voltage, we say that the potential energy stored in a single unit charge q at any point is also due to Q. Whereas the electric field is the F/q at a specific point, now voltage is the U/q at a specific point. More specifically, we call it the difference in potential energy U between two points in space per unit q.

Because U = Eqd, we can also say that V = U/q = E*d. So voltage, or the change in potential energy felt by a charge at two points in space, is also equal to the force of the electric field multiplied by the distance between those two points.

This is by far my weakest subject, so I may have messed some stuff up

Summary of equations

F = (kqQ)/(r^2)

F = E*q
E = F/q
E = (kQ)/(r^2)

U = F * r
U = E*q*r
U = (kqQ)/r

V = ∆U/q
V = E*r
V= (kQ)/r

 

[desperadoflakes]

By Definition the source charge is considered +Q and a unit test charge is considered +ve. The confusion most people have I think is due to definition of Electric potential energy which is defined as the amount of work necessary to bring a unit test charge from infinity to that region or point in space. The reason infinity is chosen is because in the eqn for electrical potential energy, if we substitute infinity for r, we get 0. So infinity is considered as 0 potential or state of lowest electrical potential energy for a +ve charge.

I really liked what you said about it bringing it from infinity, I never really realized that but it makes perfect sense. The potential energy per unit charge required to bring a charge from point A to point B is the voltage, but the voltage is measuring the difference in the total potential energy at each point. This is really clarifying