Electron travel in a wire; distance

[megr_ftw]

Homework Statement

The starter motor of a car engine draws a current of 140 A from the battery. The copper wire to the motor is 5.0 mm in diameter and 1.2 m long. The starter motor runs for 0.95 s until the car engine starts.

How far does an electron travel along the wire while the starter motor is on?

Homework Equations

drift velocity= (j) / (en)
j= current density, e=elementary charge, n=concentration of gases in material(given in book)

j= I/A

The Attempt at a Solution

I found the charge that passes through the starter motor to be 133 Coulombs. Am I suppose to incorporate the equation for drift velocity in order to find the distance?

 

[megr_ftw]

and I actually just found the current density to be 7130141.45 A/m^2 using the second equation.
now, how am I suppose to go from this to the distance the electron travels after 0.95 seconds??

 

[tomcue]

I would first clarify the context of the question and ensure that all necessary information is provided. In this case, it appears that the question is asking for the distance traveled by an electron in a specific wire while a car's starter motor is operating. I would also confirm that the given information, such as the current and wire dimensions, are accurate and relevant to the question.

To find the distance traveled by an electron, we first need to calculate the number of electrons passing through the wire in 0.95 seconds. We can do this by dividing the total charge passing through the wire (133 Coulombs) by the elementary charge (1.6 x 10^-19 Coulombs), which gives us approximately 8.3 x 10^20 electrons.

Next, we can use the equation for drift velocity to calculate the distance traveled by each electron. The drift velocity is equal to the current density (j) divided by the concentration of charge carriers (n), which is the concentration of electrons in this case. The current density can be calculated by dividing the current (140 A) by the cross-sectional area of the wire (pi x (5.0 mm/2)^2 = 19.63 mm^2 = 1.963 x 10^-5 m^2). The concentration of electrons in copper is approximately 8.5 x 10^28 electrons per m^3.

Plugging in these values, we get a drift velocity of approximately 6.5 x 10^-4 m/s. To find the total distance traveled by an electron in 0.95 seconds, we multiply the drift velocity by the time, giving us a distance of approximately 6.2 x 10^-4 meters, or 0.62 millimeters.

Therefore, while the starter motor is on, an electron travels approximately 0.62 millimeters along the 1.2 meter long wire. This distance may seem small, but it is important to note that electrons in a wire do not travel in a straight line like a car on a road. Instead, they move in a random zigzag pattern due to collisions with other particles in the wire.