Current & Drift Velocity

Charge

Let us begin with some basic ideas about the very nature of electricity. Certain particles have the property of being charged and the properties of charged objects can easily be investigated - the study of electrostatics. By convention we say that particles called electrons have a negative charge and particles called protons have a positive charge. Ions are are atoms that have become charged by either gaining or loosing an electron making them either negative or positive. A non conducting object such as a plastic ruler can become charged if (usually) electrons are transferred to or from the object, for example a balloon rubbed on your hair will gain or loose electrons due to the physical forces, involved in rubbing, dislodging some electrons. It will become charged and can be made to stick to the ceiling.

The the symbol for charge is (Q) and the unit of charge is the Coulomb (C).

Careful measurements have determined that the charge on the electron is always e = 1.6 x 10-19 C which is a very small number.
The charge on the proton is exactly the same as that on the electron only positive.
This means that 1C of charge is equivalent to 6.25 x 1018 electrons.
In electrostatics we deal both with the very small and the very large.

Current

The transfer of charge (i.e. moving charge) is called current. More specifically electric current is the rate of flow of charge i.e. the amount of charge passing a given point in a circuit each second.
The unit of current is the Ampere (A) and 1 Amp is therefore 1 Coulomb of charge passing each second. 1 A = 1 C / s
This is summarized by the equation:

I=Q/t

A current is caused by a voltage source making the electrons (or charge carriers) physically move around a circuit and so the flow of current is a dynamic process. Imagine a classic analogy, that of water moving through a pipe, the electrons in a wire are analogous to the water particles in a pipe because they move from one place to another. The charge carriers are attracted to the positive side of the battery (or whatever power supply is making them move) and repelled from the negative side. The forces that cause a current are simple electrostatic forces.

We shall see later that the charge carriers themselves move really very slowly and there are an awful lot of them in a good conductor however the 'knock on' effect is very fast, when one is made to move it bumps into its neighbour making that one move etc etc. The electrical effects that we observe, such as lights coming on immediately the switch is closed, are due to this 'knock on' effect and this explains the observation that a complete circuit is needed for current flow because if one charge carrier cannot cross a gap in the circuit all the other charge carriers behind cannot move either and current does not flow anywhere in the circuit.

Note: It is usual to use the term charge carriers to describe the particle that physically move when a current flows. In metals these charge carriers are electrons, in semi-conductors they may be electrons or 'holes', in an ionic solution both positive and negative ions move and in a gas both electrons and ionised gas particles move.

Drift velocity and the transport equation

Let us consider what is actually happening as a current flows through a material. The charge carriers (which are usually, but not always, electrons) have a charge (q) and move through the material at a velocity (v). This velocity is called the drift velocity. Within the material not all the charged particles are free to move, the carrier density (n) is the number of charge carriers free to move per cubic meter.

Remember that an electric current is the total amount of charge passing a given point per second
In one second the charge carriers travel a distance v (distance = velocity x time)
Assume the material has a cross sectional area of (A)
Therefore a volume A x v of charge carriers passes a given point each second
The number of charge carriers passing a given point each second is therefore nAv
Thus the total charge passing each second is nAvq - this is the current

I=nAvq

This is known as the transport equation

Obviously different materials have differing values for (n) and (v) - this is the reason why some materials are good conductors and other are poor.

For metals: n=1029 electrons per m3 and v=10-6 m/s
For semi-conductors: n=1018 charge carriers per m3 and v=10 m/s


Links

A Java demo of electrons flowing in a filament bulb
This java demo is copyright protected and so is not reproduced in the javalab


Transport Equation and Current Problems

1. Calculate the drift velocity in a piece of wire where the current is 1 A, the free electron density is 5 x 1028 m-3 and the diameter of the wire is 1mm. HINT: Assume the wire is circular in cross section and calculate the cross sectional area in m2, then use the transport equation to find v.

2. Calculate the drift velocity of the charge carriers in a sample of semi conductor which is 5mm wide and 2mm thick if the current is 10mA and the carrier density is 6 x 1023 m-3.

3. Calculate the drift velocity of electrons in a sample of copper which has the same dimentions as the semi conductor in question 2 and also carries a current of 10mA. For copper n = 6 x 1028 m-3.

4. In terms of the structure of a metal (such as copper) and a semi conductor (such as silicon) explain why the carrier densities are so different.

5. A potential difference of 12v is causing electrons to flow through a wire so that 1.4 x 1020 electrons pass a point in the wire in 1 minute
a) Calculate the charge that passes a given point in 1 minute
b) Calculate the current flowing in the wire
c) Calculate the resistance of the wire



Answers: 1. 1.6x10-4 m/s, 2. 0.01 m/s, 3. 1.04x10-7 m/s, 5. (a) 22.4C (b) 0.37A (c) 32.1ohms