Question

You have a section of gold wire with constant cross-sectional area. In 380 microseconds there are 10^16 electrons flowing in with drift speed 8.0 x 10^-4 m/s. What is a side length of the wire if the wire has a square cross-section?

Answer 1

Answer : Given problem ,no.of electrons ,n = 10^16

time , t = 380 microseconds = 380 * 10^-6 seconds

drift velocity V(d) = 8 * 10^-4 m/s

given wire has square cross-section. so area , A = a^2 m^2

where a is side length of the wire.

we know that current ,I = neAV(_d)

_{where e is charge of the electron. But current I = ne/t}

_{therefore ne/t =}  neAV(_d)

_{A = 1 / t*} V(_d)

_{a^2 = 1 / t *} V(_d)

_{a = square root of (1 / t *}V(_{d) )}

  _{a = square root of} ( 1 / 380 * 10^-6 * 8 * 10^-4)

a = _{square root of} ( 10^10 /3040)

a = 1813.69 m.