- #1

- 49

- 15

## Homework Statement

A current of 1600A exist in a rectangular (0.4 x 16 cm) bus bar. The electrons move at an average velocity of

*. If the concentration of electrons is 10*

**v**^{29}per cubic meter, and they are uniformly distributed, what is

*?*

**v**__Knowns__

- Current (
) = 1600A*i**= 1600 x 10*^{18}aA - Charge per Electron (
) = 1.6022 x 10*e*^{-19}C =*0.16022 aC* - Area of Cross-Section of Bar
*(*) = 0.4 (*A*) x 16 cm (**w**) =**h***0.004 x 0.16 m*-->*A = w x h*

__Unknown__

- Velocity of Current (
)*v*

## Homework Equations

- Current = Charge Moving Through a Cross-sectional Area per Unit Time -->
*i = C/t* - Number of Electrons Passing Through Said Cross-Sectional Area Per Unit Time (
) = Current / (Charge / Electron) -->*N**N = i / e* - Volume of a Rectangle (
) = Length (**V**) x Width (**l**) x Height (**w**) -->**h**-->**V = l x w x h***l = V / (w x h)* - Speed = Distance / Time

## The Attempt at a Solution

Ok, just to state this beforehand, my issue is that the velocity I end up getting seems way too low.

To help visualize this problem, I drew this:

(

*in case that doesn't work, here is the link.)*

That's the rectangular bar; I'm calling the longest part of the bar the

*length*and the other two sides, which are given (

*0.4cm by 16cm*),

*width*and

*height*respectively. Since we're given the density of electrons relative to a cubic meter, that section from the left of the bar to the cross-section is

*1 cubic meter*of the bar. The length of this section is

*. I am calling the*

**l***length of the volume of electrons cleared per second*as

*. This is all obviously not drawn to scale, but just to help visualize.*

**x**My approach is:

- Find the number of electrons that go through that given cross-sectional area per second
given the current*N*at*i**1600A* - Find the length
of a cubic meter of the bar (**l***<-- actually realized this step is not needed in my approach*) - Find how much of the volume of the bar is cleared per second
based on the results of step 1 and the density of electrons we're given (*V**10*).^{29}per cubic meter - Find the length
of that volume using volume formula and two known lengths*x**0.004m*and*0.16m*. - Since we've been setting the time at
*1s*,.**v = x / t = x / (1s) = x m/s**

, so that is**N = 9.9862 x 10**^{21}*9.9862 x 10*.^{21}electrons moving through any given cross-section per second, so that is**l = 1562.5m***1562.5 meters of length per cubic meter of volume (--> again, this was not needed in the end*)., so that is**V = N / (10**^{29}/ m^{3}) = 9.9862 x 10^{-8}m^{3}*9.9862 x 10*.^{-8}m^{3}cleared every second from the bar.**x = V / (0.004m x 0.16m) = 1.56 x 10**^{-4}.**v = 1.56 x 10**^{-4}m/s = 156 µm / s

Before you answer, the only solution I've seen after checking this forum, Chegg, and Yahoo Answers, is people using the fact that

**, then solving for**

*i = C/t**t*and setting the charge to be the charge of an electron, then using that in

**(**

*v = x/t**using the x as I've defined above*). That can work, and I'll go through that approach in this paragraph, but the way I've seen it done, people assume

*x = 1562.5m*, or the likes, which seems to me a wrong assumption. The

*t*you would get there is the amount of time it takes for the charge equivalent to an electron to pass through, which you can assume indicates 1 electron passing through, but the assumption that that the electron started out at

*x*distance from the cross-sectional area is totally random. It could have been

*1 ym*away and that still wouldn't break any rules as far as we're given.

*The only way that approach works is if you knew how far the next electron from the cross-sectional area was.*Using the density given in the problem, and the fact that we can assume

*uniform distribution*, that would give us

*, which would give us*

**1 electron per 10**^{-29}m^{3}*. Solving for time using*

**x = 1.56 x 10**^{-26}m**-->**

*i = C/t***gives us**

*t = C/i**. Using*

**t = 1.0013 x 10**^{-22}s*x*and

*t*,

*.*

**v = x / t = 1.56 x 10**^{-4}m/s = 156 µm/s*Same deal here...*

If the approach isn't wrong, then what's going on here? Shouldn't electrons be moving near the speed of light?