I = Avnq Where am i going wrong?

[SMBeresford]

Homework Statement

Find the drift velocity in a copper fuse wire with a diameter of 0.22mm. The current is at 5A.

Electronic charge is always 1.6*10^-19
Number of de-localised electrons per cubic meter in copper = 1*10^-19

Homework Equations

I=Avnq
Current = cross-sectional area*drift velocity*number of de-localised electrons*Electroic Charge

The Attempt at a Solution

First i converted the diameter of 0.22mm into radius 0.11mm. Then using pi*r² i have 3.8mm². Then i converted this into SI to make it 3.8*10^-3m².

So at this point here is the infomation i have.
I=5A
A=3.8*10^-3m²
v= ?
n= 1*10²⁹
q=1.6*10^-19

I then re-arranged the formula of I=Avnq to make v the subject.
v= __I__
Anq
Then putting in all the numbers i have...

v= ______5______
3.8*10^-3m² * 1*10²⁹ * 1.6*10^-19

Tapping this into my calculator got me the answer of 8.2*10^-8ms^-1

However this is crazy slow, i know drift velocity is very slow but not this slow. Looking at the answer in the back of the book, for somereason they put it in mm not m, 8.2mms^-1. So this in SI should be 8.2*10^-3ms^-1. This means at some point in my calculations i am 1*10⁵ wrong.

Me and and friends doing this work have been struggling to find out why we are not getting the correct answer. I hope i made sense explaining this to you. We think our errors must be around finding the cross-sectional area, or we had the wrong infomation to begin, such as the number of de-localised atoms in a cubic meter of copper. Or just some mess up of the numbers along the way. Thanks to the people who can help us out here.

 

[alphysicist]

Hi SMBeresford,

Homework Statement

Find the drift velocity in a copper fuse wire with a diameter of 0.22mm. The current is at 5A.

Electronic charge is always 1.6*10^-19
Number of de-localised electrons per cubic meter in copper = 1*10^-19

This number does not look right (but I see you are using a different number below).

Homework Equations

I=Avnq
Current = cross-sectional area*drift velocity*number of de-localised electrons*Electroic Charge

The Attempt at a Solution

First i converted the diameter of 0.22mm into radius 0.11mm. Then using pi*r² i have 3.8mm².

I don't think this is correct. If you are multiplying pi times (0.11mm)², you don't get 3.8mm².

Then i converted this into SI to make it 3.8*10^-3m².

There is a problem with the conversion here. Remember that:

$$1 \mbox{mm}^2 \neq 0.001 \mbox{m}^2$$

because the mm are squared. What would 1 mm² be if you converted to m²?

 

[SMBeresford]

Ah yes okay, so pi(0.11mm)² is actually 0.038mm²

Looking back at my original answer I was quite close really, i had the right numbers but i had the wrong powers of 10. I'm expecting to get 8.2*10^-3m s^-1 but i was actually getting the same but *10^-8...

I see your very good point about how mm² does not go into m² by just dividing by 100. Seems like an obvious mistake :P

Sooo, back to your question of what 1mm² is in m². It still should have 1 as the diget, but a different power of ten. I've tried a lot of different things but I am still not sure... what does 1mm² convert to in m? my best guess so far has been 0.000001m² but that still seems wrong and makes things worse when i did the same method in the question...

oh an also hello to the physics forum
thanks

 

[alphysicist]

Sorry, I did not see your reply until now with the server move.

Ah yes okay, so pi(0.11mm)² is actually 0.038mm²

Looking back at my original answer I was quite close really, i had the right numbers but i had the wrong powers of 10. I'm expecting to get 8.2*10^-3m s^-1 but i was actually getting the same but *10^-8...

I see your very good point about how mm² does not go into m² by just dividing by 100. Seems like an obvious mistake :P

Sooo, back to your question of what 1mm² is in m². It still should have 1 as the diget, but a different power of ten. I've tried a lot of different things but I am still not sure... what does 1mm² convert to in m? my best guess so far has been 0.000001m² but that still seems wrong and makes things worse when i did the same method in the question...

That's the correct number. 1 mm²=10^-6m². When I used that it gave me the correct answer to your problem.

The way to think about it is that to convert mm to m, you divide by 1000. Now 1 mm² is 1 mm*mm, so you have to convert two factors of mm, so you have to divide by 1000 twice.