The number density is the number of free electrons per unit volume of a material. Conductors have a high number density and insulators have a very low number density with semiconductors in between. The mean drift velocity is the average speed at which electrons move towards the positive terminal.
Equations
Description
equation
Electric current
I=Anev
Constants
constant
symbol
value
elementarycharge
e
1.6×10−19C
Variable definitions
quantity name
symbol
derived units
si base units
current
I
A
A
area
A
m2
m2
numberdensity
n
m−3
m−3
meandriftvelocity
v
ms−1
ms−1
Conductors, semiconductors and insulators
Materials can be classified into the following three groups.
Conductors
Materials that facilitate the flow of electrons and have a high conductivity.
Insulators
Materials that have a very low conductivity as they prevent the flow of energy between two objects.
Semiconductors
Materials that have a moderate conductivity falling between conductors and insulators.
These three types of material can be classified according to their number density. The number density is the number of free electrons per unit volume. The higher the number density, the more conductive a material is as it has more free electrons that can carry charge.
Mean drift velocity
When electrons flow through a wire they move randomly but tend to drift towards the positive terminal, the speed of this drift is called the mean drift velocity. Since current is the rate of flow of electrons it is possible to find it by simply knowing how many electrons cross a section of the wire per second, hence we can use the formula:
I=Anev
Exam tip: This is the only equation with mean drift velocity, if you have a question on this topic chances are you will need it!
The number density multiplied by the volume gives the total number of electrons and volume per second can be written as area times velocity, hence you can find the current with this formula.
Note: The mean drift velocity is not the speed of individual electrons but the average speed of all the electrons in the direction of the positive terminal.
Example
A copper wire has a cross sectional area of 4×10−8m2 and a number density 8.5×1028m−3. Calculate the current when electrons flow through it with a mean drift velocity of 1.8×10−3ms−1.
Firstly, write down all the known values:
Anv=4×10−8m2=8.5×1028m−3=1.8×10−3ms−1
Next, write down the equation for current:
I=Anev
Substitute all the values into the equation:
I=4×10−8×8.5×1028×1.6×10−19×1.8×10−3
Calculate the current:
I=0.98A
The current flowing through the wire is 0.98A.
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FAQs - Frequently Asked Questions
What is the number density of a material?
The number density of a material is the number of free electrons per unit volume in that material.
What is the mean drift velocity?
The mean drift velocity is the average speed of electrons moving towards a positive terminal in a circuit.
What is the difference between conductors, semiconductors and insulators?
Conductors are materials that facilitate the flow of electrons and have a high conductivity. Insulators are materials that prevent the flow of energy between two objects and therefore have a very low conductivity. Semi conductors are materials that have a moderate conductivity falling between conductors and insulators.
