Electrostatics - Current!, Convection & Conduction part 1
Although the thread is part of the Electrostatics topics, current is NOT static.
It will be discussed in 2 parts ar the word length is only 10000 characters long.
There are two types of current, namely Conduction Current and Convection Current.
Conduction Current is a movement ('flow') of charges due to the presence of an electric field.
Convection Current is a movement ('flow') of current with the absence of an electric field, the charges in a cloud could move due to the wind for example.
What will be described shortly is Convection Current and Convection Current Density. To help in understanding what is about to be discussed I recommend drawing a 3D box and lable the height (h), length (l) and width (w), h, l & w are 1 unit long. You don't have to draw the box with these dimensions but just say that they are.
The use of this 3D box will become apparent shortly.
We must now define current, well current is a movement of charges and if we wish to determine the current which flows through something we must define the area in which it flows. This is where our box comes in.
Our box has a surface area Δs, now Δs = h * w
Our box also has a volume Δv, now Δv = l * w * h
Now in order for a current to flow there must be some charge present - well naturally there will be some charge already in our box so we will use this to carry out our investigation.
Imagine that the box which you have just drawn is a part of a much bigger box. As stated above there is already charge present in our box (of unit dimensions). From our small box we can determine how much charge is present in the whole box which we are a part of.
Lets say that there are 6C of charge in our unit box, well if there are 6C of charge in 1 box then in two boxes there must be 12C of charge. To express this generally let Nq (q is subscript) be the amount of charge in Coulombs and Δv be the volume of our unit box then we can write that the total charge ΔQ = NqΔv .
The charges in our box are able to move by 'Convection' for example wind or heat. Now these charges when they move will have a velocity, lets represent this velocity as
vz (z is subscript) used z just to represent direction as not to confuse with the volume Δv.
Well as we know velocity is a measure of distance covered over time taken. For example if a ball moved 6 meters in 2 seconds the velocity would be 6/2 = 3 meters per second.
But in our case this deistance covered will be the length of our box, so we could say that the velocity is the length our charge moves over the time taken for it to move. In this case then
vz = l/t (note l = lower case L and not a 1[one])
You will need to think carefully, now put your thinking caps on! Another way of representing our volume Δv would to write Δv = Δs vz Δt. To explain this formula then, well as we wrote before Δs was our surface area h * w , well our volume is expressed by l * h * w isn't it to get just the length from our velocity vz we must multiply by t, to remove the t from the bottom of l/t to leave us with l. Thats how we got
Δv = Δs vz Δt.
Last edited by Nirvana; 09-04-2006 at 06:38 PM.
Electrostatics - Current!, Convection & Conduction part 2
So as we found before ΔQ = NqΔv we can use our re-write of Δv to get. ΔQ = Nq Δs vz Δt Coulombs.
This gives us the amount of charge, it would be more usefull to know the abount of charge there is over time. So If we divide our formula by Δt we get.
ΔQ/Δt = Nq Δs vz
Well current must be charge which flows and flows against time. In a different perspective current is the amount of charge which passes a certain point in a certain amount of time. If the charge didn't move past a point at any time then there can't be a curent - nothing is flowing.
So I = ΔQ/Δt = Nq Δs vz
Or I = Q/t
From our dicussion above it may be interesting to note the following. Current depends on the number of charges per unit volume. The less charges - the less current.
Current is directly proportional to the charge velocity vz, So the faster the charges move the more current there is.
The current depends on the charge of the particle - most likely an electron.
The current depends on the surface , the bigger the surface the bigger the current - more current can fit through at any time.
Also notice that the current has units of coloumb per second, and the charge Q = ampere . second in SI units but we use Couloms in honour of Mr Coulomb.
|conduction, convection, current, electrostatics, part|
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