Charge and current density

Oscar6330

Can we make a mathematical (equation) relationship between Current Density and Charge Q.

quZz

hmm... it seems to me that without any additional information it is only possible to connect dQ/dt with j.

Oscar6330

I am trying to find Q using a relationship in which there is no area A.

Knows are

electric potential U

Total flux density D

Total Field Intensity E

Current Density

Inductance.

Phrak

There is a relationship between charge density and current density; the charge continuity equation.

quZz

Oscar6330, could you please be more specific? What is the physical system you are trying to describe? For instance, A is area of what? U is electric potential between what points? and so forth...

naturale

In a relativistic theory charge density and spatial current density form a four vector current density j_\mu. In the non relativistic limit they are related by the continuity equation.

Oscar6330

I am trying to find out the capacitance of a system. Now C=Q/V. I am using a Simulation software. The only output parameters available are

electric potential U

Total flux density D

Total Field Intensity E

Current Density J

Inductance.

I am really stuck with it and need help as I am not a Physics guy. Pl tell me some equation

quZz

I don't quite understand...
What is total field intensity? at what point? and what is flux density?
If field intensity E is known on the surface S of the conductor you can integrate it over the surface to get total charge Q (Gauss's law)
[tex] $ Q = \varepsilon_0 \int_{S} E_n dA$ [/tex].
Capacitance C is then C = Q/U.
I have a feeling that flux density is just [tex] $ \textbf{D} = \varepsilon_0 \textbf{E}$ [/tex] so [tex] $ Q = \int_{S} D_n dA$ [/tex]
But I'm not sure...
May be capacitance of your system has already been calculated by someone? =)

Oscar6330

LOL....well since this is not an assignment, so no one has solved it. So the problem still remains unsolved

Phrak

It's a relativistic equation as well. The charge continuity equation is Lorentz invariant, and more, is covariant without connections on a curved spacetime.

naturale

Ok. what i mean is that in the non relativistic limit the charge density is give by j_0 \propto |\phi^2| and it can be associate to a quantum probability but in the relativistic limit the charge density it is not positively defined and thus it is not consistent with a probability interpretation. J_0 \propto \phi* (d_t \phi) - (d_t \phi*) \phi.

Phrak

I don't know what a relativistic limit is. Usually you want to keep things at v<c. That way it all works out, is that Maxwell's equations are true, relativistic equations. The charge continuity equation is a direct mathematical consequence, and therefore relativistically invariant itself.

Oscar6330

To be honest, I cannot understand where its going. Can you guys please redirect to my topic

naturale

you are right. the relativistic interpretation of the charge density as a probability can be the object of another topic.

Phrak

Sure, Oscar. Without a little more to go on, we don't know what to go on. You need to explain your system.

Phrak

That sounds interesting. Why don't you start a thread?

Oscar6330

Well it is very simple. I want to compute capacitance C. Now from my simulation software i can only get the following outputs, which are

electric potential V

Total flux density B

Total Field Intensity H

Current Density J

Inductance.

So I just want an equation, which has these variables only to calculate Capacitance (and some constants)