MadSci Network: Physics
Query:

Re: What is the exact, precise definition of electric charge, if any?

Date: Thu Jul 20 16:00:53 2006
Posted By: Keith Jones, Head of Physics/Deputy Head, Rhyl HS
Area of science: Physics
ID: 1153266844.Ph
Message:

Hello Pankaz,

The ampere is one of the 7 SI base units, along with metre, kilogram, 
second, kelvin, candela and mole.  The ampere is the current, which if 
flowing in two infinitely long, straight, parallel wires, one metre apart 
in a vacuum, produces a force between the wires of 2 x 10^7 newtons per 
metre length.  The coulomb is then the charge transported per second by a 
current of one ampere.  

To be more precise 

S I DEFINITION OF THE COULOMB

There is nothing cyclic about 1C = 1As. That is a definition.

1A = 1C/s is a consequence of that definition but it is not the 
definition of the ampere.

S I DEFINING EQUATION FOR QUANTITY of CHARGE

There is nothing cyclic about Q = integral I dt.         

I = dQ/dt is a consequence of that definition but is not the definition 
of I.

CONCEPT OF CHARGE

This is another matter. To me the concept of charge is more fundamental 
than that of current. The concept of charge has to be built up by 
experience. In summary it is that property of matter that gives rise to 
the forces we call electric forces. I regard current as rate of flow of 
charge.

The problem is that it is easier to measure currents than charges. Hence 
SI makes current a fundamental quantity starts with a definition of I, 
the intensity of a current, and the ampere, the unit of measure of the 
intensity. 

DEFINITION OF INTENSITY OF CURRENT AND THE AMPERE

This is complicated; which is why the average text book keeps it dark.

The general equation for the force between two current elements in a 
vacuum is: 

dF = (mu-vacuum) I1 I2 [ ds1 x ( ds2 x r ) / 4 (pi) r^2]        
where ds1 = vector length of current element number one and
r = displacement between elements.

Putting (mu-vacuum) = 4 (pi) x 10^-7 newtons/ ampere^2 defines the ampere.

The schoolboy definition uses a calculation based on the above for the 
force/length, (that is F/L) between two infinitely long thin straight 
parallel wires, a distance r apart, in a vacuum, carrying identical 
currents.
The schoolboy defining equation is	
I = [F r / L ( 2 x 10^-7)(newtons/ampere^2) ].

This makes one ampere the current which when passing through each of two 
long, straight, thin, parallel wires, one metre apart in a vacuum, gives 
rise to an attractive force between them of 2 x 10^-7 N per m of their 
length.

ALTERNATIVE SYSTEM (not SI)

However one can define Q, the Quantity charge using a similar thought 
experiment to that used to define the I, the Intensity of a current. In 
such a system 

Q is defined by the magnetic force between moving point charges

F = (mu-vacuum) Q1 Q2  v1 x (v2 x r^ )/ 4  r^2           
[v1 x (v2 x r^)is a vector product and r^ is a unit vector from one 
charge to the other.]

With identical charges

Q =  [  4 (pi) r^2  F   /   (mu-vacuum) Q1 Q2  v1 x (v2 x r^ )]^0.5       

And the I = dQ/dt



Now of course, if you are asking - what is the nature of charge? - that's 
a completely different question and one for which the answer would be a 
candidate for a Nobel Prize!

Hope this helps

Keith


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