Relating Current Density and Drift Speed

[Oijl]

Homework Statement

The figure shows wire section 1 of diameter 4R and wire section 2 of diameter 2R, connected by a tapered section. The wire is copper and carries a current. Assume that the current is uniformly distributed across any cross-sectional area through the wire's width. The electric potential change V along the length L = 1.95 m shown in section 2 is 13.5 µV. The number of charge carriers per unit volume is 8.49 1028 m-3. What is the drift speed of the conduction electrons in section 1?

Homework Equations

J = nev
v here represents the drift speed
E = pJ
E= V/L
i = nAev
J = i / A

The Attempt at a Solution

I included a lot of equations on the basis that they have some of the known quantities in them.

I can't really see how to move from knowing what the problem gives me to come up with the drift speed.

I'm given n, the number of charge carriers per unit volume, and the only equations I have that have n in them are J = nev and i = nAev.

So I would need to know J, right? So
J = E / p
and
p = (V/L) / (i/A)
and since i = nAev (and since E = V / L)
I can write
nev = (V/L) / ((V/L) / (nAev)/A)
but then the v cancels out.

So I've gotten no where.

 

[willem2]

You can look up the resistivity of copper. You can compute E in section 2 from the potential difference and length of section 2 that are given.

 

[tomcue]

I would suggest starting with the basics and using the relationship between current density and drift speed, J = nev. From the given information, we know the value of n, so we can rearrange the equation to solve for v, the drift speed.

J = nev
v = J / ne

Next, we can use the given value for the current density, J, to calculate the drift speed in section 1.

J = i / A
v = (i / A) / n

We can then use the given value for the current, i, and the cross-sectional area of section 1 to solve for the drift speed, v.

v = (i / (nA)) * (1 /A)

Finally, we can use the given value for the electric potential change, V, and the length of section 2, L, to calculate the current, i, using the equation E = V/L.

i = E * A / v

Substituting this value for i into our equation for v, we can solve for the drift speed in section 1.

v = (E * A / (nA)) * (1 / A)

Therefore, the drift speed of the conduction electrons in section 1 is v = (E / n).

In conclusion, by using the relationship between current density and drift speed and the given information about the wire, we can calculate the drift speed in section 1.