How Does Electron Drift Speed Affect Current Flow in Copper Wires?

[carus88]

A copper wire is carrying a current of 1 mA. How many electrons pass a point in the wire in one minute? If the radius of the wire is 1 mm, calculate the magnitude of the current density. Given that the number of conduction electrons in copper is 8.47 × 10^28 m-3, what is the drift speed of the electrons? A five metre length of this wire is used to connect the positive terminal of a battery to a light bulb via a switch, and a further 5 m length is used to link the other side of the bulb to the negative terminal of the battery. When the switch is closed, how long does it take on average for an electron to travel from the battery to the bulb? Why does the light come on much more quickly than this time would suggest?


1. Q=It
2. Vd= I/nqA
3. J = nqVd
4. so J equates to = I/A

For the first part i used equation 1. and then divided the answer by the charge on an electron. this gave me 3.75 x 10^17 electrons which i believe is right

The 2nd part asks for the drift velocity so i used 2.

and got 1x10^-3 / 8.47x10^28 x 1.602x10^-19 x (2x(Pi)x0.001^2)
This equalled 1.17x10^-8 ms-1

According to the answers this is in correct and should be 2.36x10^-8 ms-1

And using 4. i worked out J = 1x10-3/(2x(Pi)x0.001^2) = 159Am-2

Where as again the answers differ and it says J is 318Am-2

CAN ANYONE SHOW ME WHERE I AM GOING WRONG?

THANK YOU FOR YOUR TIME.

 

[Kurdt]

and got 1x10^-3 / 8.47x10^28 x 1.602x10^-19 x (2x(Pi)x0.001^2)
This equalled 1.17x10^-8 ms-1

The area of a a circle is not $2\pi r^2$.

 

[baba89]

I can provide some clarification on your calculations. First, for the number of electrons passing a point in one minute, your calculation is correct. The current of 1 mA means that 1x10^-3 Coulombs of charge passes through a point in the wire in one second. In one minute, that would be 60 seconds, so the total charge passing through that point in one minute would be 1x10^-3 x 60 = 6x10^-2 Coulombs. Dividing this by the charge on an electron (1.602x10^-19 Coulombs) gives you the number of electrons, which is 3.75x10^17.

For the second part, your calculation for drift velocity is incorrect. The equation Vd=I/nqA is used to calculate the average drift velocity of an electron in a specific direction. In this case, we are given the current and the number of electrons per unit volume, so we can use the equation J=nqVd to calculate the current density. Rearranging this equation to solve for Vd, we get Vd=J/nq. Plugging in the values, we get Vd=1x10^-3 A / (8.47x10^28 m^-3 x 1.602x10^-19 C x (2x(Pi)x0.001^2 m^2)) which equals 1.17x10^-8 ms^-1. This is the correct value for drift velocity.

For the third part, your calculation for current density is also incorrect. The formula J=I/A is used to calculate the current density for a given current and cross-sectional area. In this case, we are given the current and the radius of the wire, so we can use the formula J=I/(2x(Pi)xr^2) to calculate the current density. Plugging in the values, we get J=1x10^-3 A / (2x(Pi)x(0.001 m)^2) which equals 318 Am^-2. This is the correct value for current density.

As for the final question about the time it takes for an electron to travel from the battery to the bulb, this would depend on the specific conditions of the circuit and cannot be accurately calculated without more information. However, the light may come on more quickly due to the flow of electric current and the speed of