Question

The average drift speed v of electrons moving through a metal conductor is given by the equation:
\[v = \dfrac{{uf}}{e}\]
Where e is the change on an electron
f is a force acting on the electron
and u is a constant.
Determine the SI unit base of u.
SI base units ………….. .

Answer 1

Hint: SI unit of force = N (Newton), charge e = coulomb (C) and velocity v = m/s. Put the units in the given equation. The drift velocity is quite small, since there are so many free charges. Given an estimate of the density of free electrons in a conductor (the number of electrons per unit volume), it is possible to calculate the drift velocity for a given current.

Complete step by step answer:
In physics a drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero.
Given that ,
The average velocity \[v = \dfrac{{uf}}{e}\] …(1)
Where e = charge on an electron
f = force acting on the electron
u = constant
So,
\[u = \dfrac{{ve}}{f}\] (from equation 1)
We know that.
SI unit of charge = coulomb (C)
SI unit of force = Newton (N)
SI unit of velocity = m/s (m/s)
So, putting the SI units of charge force and velocity we get
\[u = \dfrac{{m/s \times C}}{N}\]
Where m = meter
s = second
c = coulomb
N = Newton

Therefore the SI unit of \[u = \dfrac{{mC}}{{Ns}}\]
Hence, the SI base is \[\dfrac{{mC}}{{Ns}}\]

Note: In this type of question, we need information about the SI units of the given things. So here the dimension and unit chapter is very important. Drift velocity of electrons in a conductor is of the order of $10^{−4}$ m/s. It is very small compared to the thermal speed which is of the order of $10^5$ m/s.