Drift Speed of the Conduction Electrons

[Ayesh]

Homework Statement

An aluminum wire with a diameter of 0.100 mm has a uniform electric field of 0.200 V/m imposed along its entire length. The temperature of the wire is 50.0 C.

a) Determine resistivity
b) Current density
c) Total current
d) Drift speed of the conduction electrons

Homework Equations

p=p₀[1+ alpha (T-T₀)]
A=$$\prod$$d²/4
J=I/A
n=#carriers/volume
I=nqAVd
V=EL
Volume=AL

The Attempt at a Solution

I had no difficulties finding the answers from a) to c) but at d) I can't find it.
A friend of mine told me I had to find the length first, but I tried to find with with all the formulas I have but I can't seem to get anywhere.

 

[noel_xxiv]

do you have the answer??

 

[noel_xxiv]

we have the same question

 

[ehild]

What do the symbols I, n, q, A, V, d mean in the equation I=nqAVd?

ehild

 

[rwisz]

I would first like to commend you on your efforts in solving the given problem. It seems that you have successfully found the answers to parts a) to c) using the given equations. For part d), you are correct in thinking that you need to find the length first. The drift speed of conduction electrons is dependent on the length of the wire, as well as other factors such as the electric field and temperature.

To solve for the drift speed, we can use the equation I = nqAVd, where I is the current, n is the number of carriers per unit volume, q is the charge of a carrier, A is the cross-sectional area of the wire, and Vd is the drift speed. We can rearrange this equation to solve for Vd:

Vd = I/(nqA)

To find the length of the wire, we can use the equation V = EL, where V is the voltage, E is the electric field, and L is the length. Rearranging this equation, we get:

L = V/E

Now we can substitute this value for L into the equation for Vd:

Vd = I/(nqA(V/E))

We already have values for I, n, q, A, and V, so we can plug those in and solve for Vd. Remember to convert the diameter of the wire to its radius before using it in the equation for cross-sectional area.

I hope this helps you solve for the drift speed of the conduction electrons. Keep up the good work in your scientific endeavors!