Current through a wire help

[XodoX]

1. A copper wire has a diameter of 1 [mm]. The density of the copper atoms inside the wire is 8.47 × 1028 [atoms/m3]. What is the charge that is free to move in a one-meter length of wire?

2. Assume that a current of 1 [A] is flowing from left to right through the wire in the above
problem. How fast are the electrons moving from right to left, in meters per second? (Hint:
consider how much charge has moved past a given point, from right to left, in one second.


Hello, I got these 2 problems left unresolved. I can't figure out how to do them. Don't find an equation that might satisfy these 2 problems. Any help is appreciated!

 

[LowlyPion]

1. A copper wire has a diameter of 1 [mm]. The density of the copper atoms inside the wire is 8.47 × 1028 [atoms/m3]. What is the charge that is free to move in a one-meter length of wire?

2. Assume that a current of 1 [A] is flowing from left to right through the wire in the above
problem. How fast are the electrons moving from right to left, in meters per second? (Hint:
consider how much charge has moved past a given point, from right to left, in one second.

Hello, I got these 2 problems left unresolved. I can't figure out how to do them. Don't find an equation that might satisfy these 2 problems. Any help is appreciated!

In 1) they tell you how to find the number of copper atoms. Then if you know how many free electrons there are you might be in business.

In 2) then if you know the number of carriers (copper atoms) then maybe this will help?
http://en.wikipedia.org/wiki/Drift_velocity#Derivation

 

[nlightner]

1. To calculate the charge that is free to move in a one-meter length of wire, we can use the equation Q = nAe, where Q is the total charge, n is the number of free electrons per unit volume, A is the cross-sectional area of the wire, and e is the elementary charge. In this case, we can calculate n by dividing the density of copper atoms by the atomic mass of copper (8.47 × 10^28 atoms/m^3 / 63.55 g/mol = 1.33 × 10^21 electrons/m^3). The cross-sectional area can be calculated by using the formula A = πr^2, where r is the radius of the wire (0.5 mm = 5 × 10^-4 m). Plugging these values into the equation, we get Q = (1.33 × 10^21 electrons/m^3) × (π × (5 × 10^-4 m)^2) × (1.6 × 10^-19 C/electron) = 1.67 × 10^-15 C. Therefore, the charge that is free to move in a one-meter length of wire is 1.67 × 10^-15 C.

2. To calculate the speed of the electrons, we can use the equation v = I/nAe, where v is the speed, I is the current, n is the number of free electrons per unit volume, A is the cross-sectional area of the wire, and e is the elementary charge. We already calculated n and A in the previous problem, so we just need to plug in the values and solve for v. v = (1 A) / ((1.33 × 10^21 electrons/m^3) × (π × (5 × 10^-4 m)^2) × (1.6 × 10^-19 C/electron)) = 2.37 × 10^-5 m/s. Therefore, the electrons are moving from right to left at a speed of 2.37 × 10^-5 m/s.