# Current density question

1. Aug 17, 2008

### 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?

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