# Current density and drift velocity

In summary, the problem involves determining the current density, drift velocity of electrons, and mean time between collisions in a copper wire carrying a 4 A current. The equations used include J = I/A for current density, I = nqVdA for drift velocity, and τ = σme / nq2 for mean time between collisions. Using these equations and the given parameters for copper, the current density was found to be 318,309.89 A and the drift velocity was found to be 2.4012 X 10 -5 m/s. For the mean time between collisions, the formula τ = σme / nq2 was used and calculated to be 8.068 X 10-15 s.

## Homework Statement

1. A copper wire 2 mm in diameter carries a 4 A current. Determine the current density in the wire, drift velocity of the electrons and the mean time between collisions. Assume that each copper atom contributes one free electron. Hint: you may need some additional parameters of copper to solve this problem.

## Homework Equations

A) For current density: J = I/A
We know: A = ∏r2 m2

B) Drift velocity: I = nqVdA . thus Vd = I / (nqA)
We know: n = density/mass atom, or (8.95g/cm3 X 106 cm3/m3) / 1.05565 X 10-22g/atom = 8.478 X 1028 atoms/m3
q = 1.602 X 10-19 C

C) σ = (nqτ2)/me, thus τ = σme / nq2
and σ = 1/p, p being resistivity, and resistivity for copper is 1.7 X 10-8 ohm*m

## The Attempt at a Solution

A) ∏*0.0022m2 = 1.2265 X 10-5 m2
4 / 1.2265 X 10-5 = 318,309.89 A

B) Simply plug in the numbers: Vd = 4A / (8.478 X 1028/m3 * 1.602 X 10-19 C * 1.2265 X 10-5 m2 = 2.4012 X 10 -5 m/s

C) For C, I have no clue in which direction to go, I've browsed through my book but can't find any relevant formula

Any help for letter C would be appreciated, and also if you can check if what I did in A and B makes sense? Thank you!

Edit: I found something in the book, would the formula on C make sense?

Last edited:
τ = σme / nq2 = (1.7 X 10-8 ohm*m * 9.11 X 10-31 kg * 2.8 X 106 m/s)/(8.478 X 1028 atoms/m3 * 1.602 X 10-19 C2) = 8.068 X 10-15 s

## What is current density?

Current density is a measure of the amount of electric current flowing through a given area. It is calculated by dividing the magnitude of the current by the cross-sectional area through which it is flowing.

## How is current density related to drift velocity?

Current density and drift velocity are related through Ohm's Law, which states that the current density is directly proportional to the drift velocity and the cross-sectional area of the conductor. This means that an increase in either the current density or the cross-sectional area will result in an increase in the drift velocity.

## What factors affect the value of current density?

The value of current density is affected by the magnitude of the current, the cross-sectional area of the conductor, and the material's resistance. Additionally, temperature can also impact current density, as higher temperatures can increase the resistance of a material.

## How is current density measured?

Current density can be measured using a variety of instruments such as ammeters or multimeters. These instruments measure the amount of current flowing through a specific area and can calculate the current density using the formula I/A, where I is the current and A is the cross-sectional area.

## Why is current density an important concept in electricity?

Current density is an important concept in electricity because it allows scientists and engineers to understand and calculate the behavior of electric currents in different materials and configurations. It also helps in determining the maximum safe levels of current flow for different conductors and can aid in designing efficient electrical systems.

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