# Find the drift velocity

fishturtle1

## Homework Statement

A 5.00-A current runs through a 12 gauge copper wire (diameter 2.05mm) and through a light bulb. Copper has 8.5 x 1028 free electrons per cubic meter.

c) At what see does a typical electron pass by any given point in the wire?

J = nqvd

## The Attempt at a Solution

The previous parts of the question I solved for current density.

J = 3.105 x 106 A / m2

n = 8.5 x 1028 electrons / m3

vd = J / n|q|

I substituted all my values in:

vd = (3.105 x 106 ) / (8.5 x 1028)(1.602 x 10-28)

vd = (3.105 x 106) / 13.167 m/s

vd = 2.28 x 105 m/s

the correct answer is vd = 0.111 mm/s

I'm sorry this is probably an arithmetic error but i can't see what I did wrong

Mentor
Can you show us how you arrived at your current density?

fishturtle1
Can you show us how you arrived at your current density?

b) What is the current density?

cross section area = A = πr2 = πd2 / 4 = π(2.05x106) / 4 = 1.61 x 10-6

I = 5 A

Then current density = J = I / A = 5 / 1.61 x 10-6 = 3.105 x 106

..
Also the very first part:
a) How many electrons pass through the lightbulb each second?

I = 5A = 5 C/s

5 C/s * 1s = 5C

5C / (-1.602 x 10-28) = -3.121 x 1028 electrons

Mentor
b) What is the current density?

cross section area = A = πr2 = πd2 / 4 = π(2.05x106) / 4 = 1.61 x 10-6
You didn't square your diameter when you calculated the cross sectional area.

a) How many electrons pass through the lightbulb each second?

I = 5A = 5 C/s

5 C/s * 1s = 5C

5C / (-1.602 x 10-28) = -3.121 x 1028 electrons
Use the magnitude of the charge on the electron. The sign of the charge is unimportant if you're counting quantity, which should be a positive number.

fishturtle1
You didn't square your diameter when you calculated the cross sectional area.

Use the magnitude of the charge on the electron. The sign of the charge is unimportant if you're counting quantity, which should be a positive number.
Ok I see what you mean .. so the correct cross sectional area is:

A = π((2.05)2 x 10-3*2) / 4 = 3.30 x 10-6
J = 5 / 3.30 x 10-6 = 1.51 x 106 A / m2

So I know my J and |q| are correct..I also forgot to mention that the problem gave "Copper has 8.5 x 1028 free electrons per cubic meter" which I use as my n value.

So vd = J / n|q|.
J = 1.51 x 106
n = 8.5 x 1028 free electron / m3
|q| = 1.602 x 10-28 C

vd = (1.51 x 106) / (8.5)(1.602) = (1.51 x 106) / 13.617 = 110,890 m/s

never mind I just realized |q| = 1.602 x 10-19.. so 110,890 * 10-9 = .111 x 10-3 which is the answer in the book.

Thanks for helping me on this.

gneill