"

Set 52 Problem number 1


Problem

There are 8.7 + 10^18 current-carrying electrons which are effectively drifting along at .065 m/s in a uniform conducting wire of length 4.85 m.  What is the current in electrons/sec, and what is the current in amps?

Solution

Since electrons drift at .065 m/s, in 1 second all the electrons in .065 meters of the  wire will pass a given point.

The distance moved in a second is .065 meters, which is is .065 / 4.85 = .0134 of the length of the wire.

This increment therefore   contains .0134 * 8.7 * 10^18 = 116.5 * 10^15 electrons.

So in a second, the rate at which electrons pass the point is 116.5 * 10^15 electrons.

An electron carries a charge of approximately 1.6 * 10^-19 Coulombs, so the charge carried in a second is

Generalized Solution

If there are nElectrons current-carrying electrons in a length L of wire, and if they drift a distance `dL in one second, then in each second the proportion `dL / L of the nElectrons electrons, or (nElectrons * `dl / L) electrons will pass a given point. The electrons each carry charge 1.6 * 10^-19 Coulombs, so the current is

1.6 * 10 ^ -19 Coulombs / electron * (nElectrons * `dL / L) electrons / sec = 1.6 * 10^-19 * nElectrons * `dL / L amps.

Explanation in terms of Figure(s), Extension

The figure below shows a length L of wire containing nElectrons current-carrying electrons, and a segment of length `dL through which electrons travel in a second.

The resulting current in electrons/second is easily converted to Coulombs/second.

Figure(s)

current_and_drift_velocity.gif (4559 bytes)

"