# Derivation of drift speed question

• astropi
In summary, the conversation discusses the derivation of the drift velocity formula, which assumes an external electric field. There is a discussion about the contradiction between the assumption of a random velocity in the absence of an electric field and the assumption of an electric field in the derivation. The conversation concludes that the average velocity in the absence of an electric field is zero, but in the presence of an external electric field, the average velocity should not be zero.
astropi

## Homework Statement

First off, this is NOT a homework problem. This is a conceptual question I have regarding the derivation of the drift velocity

$$v_d =[(qE)/m] \tau$$

Typically, when this formula is derived, you first calculate the acceleration of a particle in the electric field (qE/m) and then it is noted that using v = v_o + a*t you can rearrange to get your drift velocity. However, and here is my question, it is usually noted that in the absence of an electric field the velocity of a charged particle is random and thus v_o = 0. However, this derivation assumes that the particle in a conductor experiences an electric force F = qE and thus you have to have an electric field, which I would imagine means you can NOT let v_o = 0. Am I missing something? Hopefully my question is clear, if not, I'll try to clarify. Thanks.

See above.

## The Attempt at a Solution

N/A

usually noted that in the absence of an electric field the velocity of a charged particle is random and thus v_o = 0
is not correct. It should say <v_0> = 0, meaning: the average (x-) component of the velocity of the electrons is zero. They move like crazy all over the place, though.

you have to have an electric field, which I would imagine means you can NOT let v_o = 0
is somewhat unclear to me. If you take a piece of wire and apply an emf by connecing both ends to the two ends of a battery, that emf is present, irrespective of the v0.

If it helps, you could think of a conducting wire as if it were a long pipe filled with short springs of a little less than the inner diameter: push in a spring at one end, out comes one at the other. But it takes quite a while before the spring you press in re-appears. (warning: this analogy doesn't go very far...)

Ah yes, of course, <v_o> = 0
Thanks for pointing that out. However, I think my question still holds: in the absence of an electric field the velocity of a charged particle is random and thus <v_o> = 0. However, to derive the acceleration you have to assume an electric field since F = qE. How do you reconcile the two statements? Thanks.

I have difficulty understanding where exactly do you think there is a contradiction ? The electric field comes from outside, not from the electrons themselves.

I know the electric field is external. So perhaps another way of wording the question is: <v_o> = 0 in the presence of an E-field? I don't believe that is true. That is why we say in the absence of an electric field the velocity of a charged particle is random and thus on average = 0. However, here we are assuming an external E-field and thus <v_o> should not be equal to 0.

## What is the concept of drift speed in electrical currents?

The concept of drift speed refers to the average velocity of free electrons in a conductor when an electric field is applied. It is a measure of how quickly the electrons are moving through the material in response to the applied electric field.

## How is drift speed calculated?

Drift speed can be calculated using the equation v = I/nqA, where v is the drift speed, I is the current, n is the number of charge carriers per unit volume, q is the charge of each carrier, and A is the cross-sectional area of the conductor.

## What factors affect the drift speed of electrons?

The drift speed of electrons is affected by the strength of the electric field, the density of free electrons in the material, and the cross-sectional area of the conductor. It is also dependent on the material's resistivity and temperature.

## Why is drift speed important in understanding electrical currents?

Drift speed is important because it helps us understand the behavior of electrons in a conductor and how they contribute to the flow of electrical current. It also helps in analyzing the efficiency and performance of different electrical components and circuits.

## How does drift speed relate to Ohm's law?

Ohm's law states that the current in a conductor is directly proportional to the voltage and inversely proportional to the resistance. The drift speed of electrons is directly related to the current and the resistance of the material. As the drift speed increases, the current also increases, while a higher resistance will result in a slower drift speed and lower current.

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