How can an increase in area cause a decrease in drift speed?

Tags:
1. Nov 12, 2015

MBBphys

1. The problem statement, all variables and given/known data
We have:
I=nAve
Imagine a copper wire with a constant current through it:
I=constant
e=constant
n (for copper)=constant

Hence, we obtain:

A is inversely proportional to electron drift velocity.

My question is: how does that make sense? Why would the cross sectional area increasing lead to the electron drift velocity decreasing?

Thanks
2. Relevant equations
I=nAve

3. The attempt at a solution
N/A

2. Nov 12, 2015

TSny

Suppose you had a pipe carrying water at a rate of 100 gallons per minute.

A second pipe also carries water at 100 gallons per minute, but has twice the cross-sectional area. How does the speed of the water in the second pipe compare to the speed in the first pipe?

3. Nov 12, 2015

MBBphys

Ah. Now I get it; the second pipe can carry a larger volume, so it has to reduce the speed to keep the discharge of 100 gallons per minute constant. How silly of me!

Thank you very much

4. Nov 12, 2015

Staff: Mentor

Actually, the first equation "I=constant" is sufficient for answering the question. Given a constant current, the average drift velocity of the electrons is inversely proportional to the cross-sectional area of the conductor.

The second equation "e=constant" will not be true in general when you vary the cross-sectional area of a conductor. Doing so will vary the resistance of the conductor, so to maintain a constant current I, the voltage "e" will need to change.

5. Nov 12, 2015

TSny

I believe "e" here stands for the magnitude of the electric charge of an electron.

6. Nov 12, 2015

Staff: Mentor

LOL.

If they start varying that in future problems, I'd be a little worried...

7. Nov 12, 2015