What is the average velocity of an electron

Lights come on as soon as a switch is flicked. How do we reconcile these two speeds, and what does it tell us about standard conductors?

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced into a wire, as in Figure 4, the incoming charge pushes other charges ahead of it, which in turn push on charges farther down the line.

The density of charge in a system cannot easily be increased, and so the signal is passed on rapidly. The resulting electrical shock wave moves through the system at nearly the speed of light. To be precise, this rapidly moving signal or shock wave is a rapidly propagating change in electric field.

Figure 4. When charged particles are forced into this volume of a conductor, an equal number are quickly forced to leave. The repulsion between like charges makes it difficult to increase the number of charges in a volume. Thus, as one charge enters, another leaves almost immediately, carrying the signal rapidly forward. Good conductors have large numbers of free charges in them. In metals, the free charges are free electrons.

Figure 5 shows how free electrons move through an ordinary conductor. The distance that an individual electron can move between collisions with atoms or other electrons is quite small. The electron paths thus appear nearly random, like the motion of atoms in a gas.

But there is an electric field in the conductor that causes the electrons to drift in the direction shown opposite to the field, since they are negative. The drift velocity v d is the average velocity of the free charges. Drift velocity is quite small, since there are so many free charges. If we have an estimate of the density of free electrons in a conductor, we can calculate the drift velocity for a given current.

The larger the density, the lower the velocity required for a given current. Figure 5. Free electrons moving in a conductor make many collisions with other electrons and atoms. The path of one electron is shown.

The average velocity of the free charges is called the drift velocity, v d , and it is in the direction opposite to the electric field for electrons. The collisions normally transfer energy to the conductor, requiring a constant supply of energy to maintain a steady current.

The free-electron collisions transfer energy to the atoms of the conductor. The electric field does work in moving the electrons through a distance, but that work does not increase the kinetic energy nor speed, therefore of the electrons.

Thus a continuous power input is required to keep a current flowing. An exception, of course, is found in superconductors, for reasons we shall explore in a later chapter. Superconductors can have a steady current without a continual supply of energy—a great energy savings.

In contrast, the supply of energy can be useful, such as in a lightbulb filament. The supply of energy is necessary to increase the temperature of the tungsten filament, so that the filament glows. We can obtain an expression for the relationship between current and drift velocity by considering the number of free charges in a segment of wire, as illustrated in Figure 6. The number of free charges per unit volume is given the symbol n and depends on the material.

The shaded segment has a volume , so that the number of free charges in it is nAx. Rearranging terms gives. The carriers of the current each have charge q and move with a drift velocity of magnitude v d.

Figure 6. See text for further discussion. Note that simple drift velocity is not the entire story. The speed of an electron is much greater than its drift velocity.

In addition, not all of the electrons in a conductor can move freely, and those that do might move somewhat faster or slower than the drift velocity. So what do we mean by free electrons? Atoms in a metallic conductor are packed in the form of a lattice structure. Some electrons are far enough away from the atomic nuclei that they do not experience the attraction of the nuclei as much as the inner electrons do. These are the free electrons. These free electrons respond by accelerating when an electric field is applied.

Of course as they move they collide with the atoms in the lattice and other electrons, generating thermal energy, and the conductor gets warmer. In an insulator, the organization of the atoms and the structure do not allow for such free electrons. Calculate the drift velocity of electrons in a gauge copper wire which has a diameter of 2.

Household wiring often contains gauge copper wire, and the maximum current allowed in such wire is usually 20 A. The density of copper is 8. We are given the density of copper, 8. First, calculate the density of free electrons in copper. There is one free electron per copper atom. Therefore, is the same as the number of copper atoms per m 3. We can now find n as follows:. The minus sign indicates that the negative charges are moving in the direction opposite to conventional current.

The direction of conventional current is taken as the direction in which positive charge moves. Current is the flow of free charges, such as electrons and ions. Drift velocity v d is the average speed at which these charges move. Here, I is the current through a wire of cross-sectional area A. Electrical signals travel at speeds about 10 12 times greater than the drift velocity of free electrons.

Conceptual Questions Can a wire carry a current and still be neutral—that is, have a total charge of zero? To what physical quantity do ampere-hours correspond voltage, charge,. If two different wires having identical cross-sectional areas carry the same current, will the drift velocity be higher or lower in the better conductor? Why are two conducting paths from a voltage source to an electrical device needed to operate the device?

In cars, one battery terminal is connected to the metal body. How does this allow a single wire to supply current to electrical devices rather than two wires? Contrast this with the situation in which a large bird hits two wires simultaneously with its wings. What is the current in milliamperes produced by the solar cells of a pocket calculator through which 4.

A total of C of charge passes through a flashlight in 0. What is the average current? What is the current when a typical static charge of 0. Find the current when 2. A large lightning bolt had a 20,A current and moved What was its duration? The A current through a spark plug moves 0. How long does the spark last? What is the resistance of the path? Discuss the difficulties that would ensue if a larger voltage were used to produce the same current through the patient, but with the path having perhaps 50 times the resistance.

Hint: The current must be about the same, so a higher voltage would imply greater power. Figure 7. The capacitor in a defibrillation unit drives a current through the heart of a patient.

During open-heart surgery, a defibrillator can be used to bring a patient out of cardiac arrest. What voltage should be applied? How much charge moves? See Figure 7. The wire rushing towards them hits it harder from one direction than the other.

At first they are running around in all directions at equal speeds but when they hit part of the wire that part of the wire is moving so when they hit head on they get pushed harder and when they overtake it they get pushed back less hard, the net effect is that they start to move in the direction of the wire, at the speed of the wire. So now let's bring up the electric field.

Imagine an electric field pointing in the x direction, then it wants to accelerate electrons in the -x direction. But what if the wire was moving in the x direction. If it moved at the right speed it would make the electrons move in the x direction exactly as much on spatial average as the electric field makes them go in the -x direction.

So the net effect is the electrons would move around equally in all direction. That is exactly what happens in the frame moving at drift velocity.

In that frame the electrons move equally in all direction, the wire is moving at drift velocity and there is an electric field. That is literally where the drift velocity come from. The speed of the wire relative to the average velocity of the electrons that produces as much acceleration from electron-wire interactions as the the electron gets from electron-electric-field interactions.

A very simple view of things happening inside of a conductor There is, therefore, some final speed at which friction forces and force due to electric field balance out. This speed can be viewd as the drift speed. It refers to a speed at which all of the electrons move down the conductor in the direction of the applied field. Friction forces are caused by electron-electron, electron-phonon collisions.

So, this is the way energy is lost due to entropy. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Average drift velocity of electron in conductor Ask Question. Asked 6 years, 7 months ago. Active 6 years, 1 month ago. Viewed 11k times. Improve this question. DanielSank Kelvin S Kelvin S 1, 3 3 gold badges 12 12 silver badges 18 18 bronze badges.

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Add a comment. Active Oldest Votes. So stronger fields just have proportionally stronger effects and changes in velocity In that sense the factor of two isn't the issue, it's just a characteristic time, and in the low field limit that characteristic time doesn't change for different applied fields.

What is the characteristic time? So what is drift velocity really and where does it come from really? How does the scattering counter the electric field? Improve this answer. Timaeus Timaeus Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.

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