# Potential difference and electric field relationship advice

### Potential Difference - Relation with Electric Field

Oct 11, Electric field vs Electric potential. An electric field is present around a charge – either negative or positive. Any charged object can also acquire. Description: To understand the relation between the potential difference and the electric field, take two points A and B in the electric field with a very small. Formal definition of electric potential and voltage. Written by Electric force and electric field are vector quantities (they have magnitude and direction). Electric.

The point is that the potential difference is because of the electrical forces in the charges. To move anything against the potential difference simply requires a force opposing the electron force. Could you mention the name of the chemical force? Do you mean to say that there's not only one single force which is provided by the potential difference? Just like the electric force is electric force. Just as the charges establish an electric potential difference, in the same way inside the battery a chemical potential difference is set up.

When this chemical potential difference causes a stronger force than the electric potential difference, the force is stronger, and the charge will be moved back. See if you can follow this train of reasoning. Note how I said reasoning and not logic. This isn't a proof. The mathematics will show how everything is related.

A difference in electric potential gives rise to an electric field. This is the concept I am introducing to you in this chapter you are reading right now.

The electric field is the force per charge acting on an imaginary test charge at any location in space. This concept was introduced in the chapter before this one. The work done placing an actual charge in an electric field gives the charge electric potential energy. This concept is called the work-energy theorem and was introduced a long time ago, in a chapter far, far away. By the transitive property I guesselectric potential gives rise to electric potential energy; and by the reflexive property another guessthe electric potential is the energy per charge that an imaginary test charge has at any location in space.

We can do this the hard way without calculus or the easy way with calculus. In any case, here are the rules for the symbols specific to this topic… The symbol for electric field is a bold, uppercase E.

It's bold because it's a vector quantity. It's uppercase because of an arbitrary choice. Thus there is no reason for the hot air below to rise; if it were to rise, it would cool to a lower temperature than the air already there, would be heavier than the air there, and would just want to come down again. The air is in stable mechanical equilibrium. On the other hand, if we think of a parcel of air that contains a lot of water vapor being carried up into the air, its adiabatic cooling curve will be different.

### The Feynman Lectures on Physics Vol. II Ch. 9: Electricity in the Atmosphere

As it expands and cools, the water vapor in it will condense, and the condensing water will liberate heat. Moist air, therefore, does not cool nearly as much as dry air does. It will cool off somewhat, but will still be warmer than the surrounding air at the same level.

If we have a region of warm moist air and something starts it rising, it will always find itself lighter and warmer than the air around it and will continue to rise until it gets to enormous heights. This is the machinery that makes the air in the thunderstorm cell rise. For many years the thunderstorm cell was explained simply in this manner. A mature thunderstorm cell. As the water vapor is carried up and condenses, it forms tiny drops which are rapidly cooled to temperatures below zero degrees.

Only if there is some small piece of material present, like a tiny crystal of NaCl, will the water drop freeze into a little piece of ice. Then the equilibrium is such that the water drops evaporate and the ice crystals grow. Thus at a certain point there is a rapid disappearance of the water and a rapid buildup of ice. Also, there may be direct collisions between the water drops and the ice—collisions in which the supercooled water becomes attached to the ice crystals, which causes it to suddenly crystallize.

So at a certain point in the cloud expansion there is a rapid accumulation of large ice particles. When the ice particles are heavy enough, they begin to fall through the rising air—they get too heavy to be supported any longer in the updraft. As they come down, they draw a little air with them and start a downdraft. And surprisingly enough, it is easy to see that once the downdraft is started, it will maintain itself.

The air now drives itself down! The moment it does that, it is denser than the environment and continues to fall rapidly. First, you argue that the air should rise, and when you have it up there, you argue equally well that the air should fall. When the situation is unstable and the warm air should rise, then clearly something has to replace the warm air.

It is equally true that cold air coming down would energetically replace the warm air, but you realize that what is coming down is not the original air. The early arguments, that had a particular cloud without entrainment going up and then coming down, had some kind of a puzzle.

They needed the rain to maintain the downdraft—an argument which is hard to believe. As soon as you realize that there is a lot of original air mixed in with the rising air, the thermodynamic argument shows that there can be a descent of the cold air which was originally at some great height.

This explains the picture of the active thunderstorm sketched in Fig. As the air comes down, rain begins to come out of the bottom of the thunderstorm.

So just before the rain comes there is a certain little cold wind that gives us a forewarning of the coming storm. In the storm itself there are rapid and irregular gusts of air, there is an enormous turbulence in the cloud, and so on.

But basically we have an updraft, then a downdraft—in general, a very complicated process. The late phase of a thunderstorm cell. Before we describe lightning, however, we can finish the story by looking at what happens to the thunderstorm cell after about one-half an hour to an hour. The cell looks as shown in Fig. The updraft stops because there is no longer enough warm air to maintain it. The downward precipitation continues for a while, the last little bits of water come out, and things get quieter and quieter—although there are small ice crystals left way up in the air.

Because the winds at very great altitude are in different directions, the top of the cloud usually spreads into an anvil shape. The cell comes to the end of its life.

Experiments of various kinds—including flying airplanes through thunderstorms the pilots who do this are brave men!

The top of the thunderstorm has a positive charge, and the bottom a negative one—except for a small local region of positive charge in the bottom of the cloud, which has caused everybody a lot of worry.

No one seems to know why it is there, how important it is—whether it is a secondary effect of the positive rain coming down, or whether it is an essential part of the machinery. Anyway, the predominantly negative charge at the bottom and the positive charge at the top have the correct sign for the battery needed to drive the earth negative.

The distribution of electrical charges in a mature thunderstorm cell. These large voltages break down the air and create giant arc discharges. When the breakdown occurs the negative charges at the bottom of the thunderstorm are carried down to the earth in the lightning strokes. Now we will describe in some detail the character of the lightning. First of all, there are large voltage differences around, so that the air breaks down. There are lightning strokes between one piece of a cloud and another piece of a cloud, or between one cloud and another cloud, or between a cloud and the earth.

This means that any model made to explain how this storm generates its electricity must be one with plenty of juice—it must be a big, rapidly operating device. A jet of water with an electric field near the nozzle. Before we go further we shall consider something which is almost certainly completely irrelevant, but nevertheless interesting, because it does show the effect of an electric field on water drops. We say that it may be irrelevant because it relates to an experiment one can do in the laboratory with a stream of water to show the rather strong effects of the electric field on drops of water.

In a thunderstorm there is no stream of water; there is a cloud of condensing ice and drops of water. So the question of the mechanisms at work in a thunderstorm is probably not at all related to what you can see in the simple experiment we will describe.

If you take a small nozzle connected to a water faucet and direct it upward at a steep angle, as in Fig. If you now put an electric field across the stream at the nozzle by bringing up a charged rod, for examplethe form of the stream will change. With a weak electric field you will find that the stream breaks up into a smaller number of large-sized drops. But if you apply a stronger field, the stream breaks up into many, many fine drops—smaller than before.

With a stronger field, however, there is an increase in the tendency to separate into drops. The explanation of these effects is probably the following. If we have the stream of water coming out of the nozzle and we put a small electric field across it one side of the water gets slightly positive and the other side gets slightly negative.

Then, when the stream breaks, the drops on one side may be positive, and those on the other side may be negative. On the other hand, if the field is stronger, the charge in each one of the drops gets much larger, and there is a tendency for the charge itself to help break up the drops through their own repulsion. Each drop will break into many smaller ones, each carrying a charge, so that they are all repelled, and spread out so rapidly. So as we increase the field, the stream becomes more finely separated.

The only point we wish to make is that in certain circumstances electric fields can have considerable influence on the drops. The exact machinery by which something happens in a thunderstorm is not at all known, and is not at all necessarily related to what we have just described.

We have included it just so that you will appreciate the complexities that could come into play. In fact, nobody has a theory applicable to clouds based on that idea. We would like to describe two theories which have been invented to account for the separation of the charges in a thunderstorm. All the theories involve the idea that there should be some charge on the precipitation particles and a different charge in the air.

Then by the movement of the precipitation particles—the water or the ice—through the air there is a separation of electric charge.

### electrostatics - Relation between Electric field and potential - Physics Stack Exchange

The only question is: How does the charging of the drops begin? Somebody discovered that if you have a drop of water that breaks into two pieces in a windstream, there is positive charge on the water and negative charge in the air. This breaking-drop theory has several disadvantages, among which the most serious is that the sign is wrong. Second, in the large number of temperate-zone thunderstorms which do exhibit lightning, the precipitation effects at high altitudes are in ice, not in water.

From what we have just said, we note that if we could imagine some way for the charge to be different at the top and bottom of a drop and if we could also see some reason why drops in a high-speed airstream would break up into unequal pieces—a large one in the front and a smaller one in the back because of the motion through the air or something—we would have a theory. Different from any known theory!

## Difference Between Electric field and Electric Potential

Then the small drops would not fall through the air as fast as the big ones, because of the air resistance, and we would get a charge separation. You see, it is possible to concoct all kinds of possibilities. One of the more ingenious theories, which is more satisfactory in many respects than the breaking-drop theory, is due to C.

We will describe it, as Wilson did, with reference to water drops, although the same phenomenon would also work with ice. The drop will have an induced dipole moment—with the bottom of the drop positive and the top of the drop negative, as drawn in Fig. The fast ions do not have an important effect here.

Suppose that as a drop comes down, it approaches a large ion. If the ion is positive, it is repelled by the positive bottom of the drop and is pushed away. So it does not become attached to the drop. If the ion were to approach from the top, however, it might attach to the negative, top side.

But since the drop is falling through the air, there is an air drift relative to it, going upwards, which carries the ions away if their motion through the air is slow enough.