8.4 Mean drift velocity

Question 1

What is number density?

Answer 1

The number of free electrons per unit volume. The higher the number density, the greater the number of free electrons per m^3 and so the better the electrical conductor.

Question 2

What are the 3 groups that materials can be classified as according to their number density?

Answer 2

Insulator
-few or no conduction electrons; number density is
almost zero.

Semiconductor
-they have number densities approximately 1 million times smaller than metals such as copper; the conduction electrons travel faster than in conductors and can be changed by adding an impurity to a material such a silicon.

Conductor
-large number density of conduction electrons

Question 3

What is drift velocity?

Answer 3

Charged particles do not travel in a straight line through a conductor, because they collide with other particles in the material. Therefore this is used as the average speed the particle travels at along the conductor.

Question 4

What equation links current to mean drift velocity?

Answer 4

current = no. of charge carriers per volume x mean drift velocity x charge

I=vAnQ

When relating the equation to current in a metal, the charge carriers are electrons therefore:
I=Anev where e = charge on an electron (elementary charge)

Question 5

What is the effect of changing the cross-sectional area of a wire?

Answer 5

The narrower the wire, the greater the drift velocity must be in order for the current to be the same.

Question 6

A piece of wire carrying a current narrows such that it radius halves. What effect does this have on the mean drift velocity of the electrons in the wire?

Answer 6

I=Anev–>v=I/(Ane)
According to Kirchhoff’s first law, the current in the wire is the same. The elementary charge e and the number density n are also constants as n does not change because the material stays the same. If the radius halves, the cross-sectional area will decrease by a factor of 4. As a result the mean drift velocity will increase by a factor of 4.