# 2. Microscopic Model of Electric Current in a Metal

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Information Report
Category:

## Electrical Engineering

Published:

Views: 2 | Pages: 2

Share
Related documents
Description
2. Microscopic Model of Electric Current in a Metal - We’ll picture the metal as a regular array of atoms plus “free” or “conduction” electrons that…
Transcript
2. Microscopic Model of Electric Current in a Metal - We’ll picture the metal as a regular array of atoms plus “free” or “conduction” electrons that move around in random directions very rapidly ( with velocities of 106 m/s, close to 1% of the speed of light!!). These electrons make a series of collisions with the atoms and ricochet in random directions – just like gas molecules in air – and , in fact, we often use the term electron gas. - In the absence of an external electric field in the wire, all the electrons move about randomly and there is no net I flowing in the wire (see Figure 27-12 on page 623 in your text). - Now, suppose an external electric field is produced in the wire – this requires an outside agent – usually a battery or power supply. Let’s imagine that the electric field is uniform in the wire. What happens? - Each electron with a charge q ( = -e) and mass me will experience a force given by G G G F = me a = qE , so that an acceleration G q G a= E will be produced. According to our kinematics equations, then me G G G v = vi + at But the electrons will make collisions with the metal atoms and the initial velocity after each collision will be random in direction. Each time an electron makes a collision with an atom, it gives up the extra kinetic energy it gained (so that the heavier atoms vibrate a bit more – we will see that this causes a temperature increase of the metal) and then moves off in a random direction. - If τ is the average time between collisions with an atom, then (where means the time average value G G q G v = vi + E t me and since the average initial velocity is zero (see just above), we have that G G q G v = vd = Eτ , where vd is the drift velocity. me We’ll see that vd is about 1 mm/s – much !! slower (9 order of magnitude) than the random velocity of the electron. - Now let’s see how to relate vd to the current flowing along the wire: With n = the number of electrons per unit volume, or density of electrons, (see sketch of wire) ∆Q (in hatched region) = nA(vd ∆t) q vd ∆t ∆Q so I ave = = qnAv d ∆t - Next, we introduce the current density, J = I/A, where A is an area perpendicular to the velocity of the charges. Then we can write that nq 2 J = nqv d = Eτ me or nq 2 J = σ E where σ = τ me σ is called the electrical conductivity and is a constant independent of E Any material that obeys this relation is said to obey Ohm’s Law.
Recommended

6 pages

6 pages

7 pages

7 pages

17 pages

26 pages

12 pages

16 pages

22 pages

78 pages

73 pages

6 pages

23 pages

36 pages

### Magnets and Magnetic Fields Electric Currents Produce Magnetic Fields Force on an Electric Current in a Magnetic Field; Definition of B Force on - PDF

29 pages

View more...

#### Military museum portugal

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x