# Charge and current density

#### Oscar6330

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

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#### 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)
$$Q = \varepsilon_0 \int_{S} E_n dA$$.
Capacitance C is then C = Q/U.
I have a feeling that flux density is just $$\textbf{D} = \varepsilon_0 \textbf{E}$$ so $$Q = \int_{S} D_n dA$$
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

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.
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

To be honest, I cannot understand where its going. Can you guys please redirect to my topic
Sure, Oscar. Without a little more to go on, we don't know what to go on. You need to explain your system.

#### Phrak

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

#### Phrak

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)
You talked about a 'system'. Is it a circuit? Is it a component? What are the dimensions? Are there changes invloved that are fast enough that all of Maxwell's equations are needed, so that B is a factor? J is current density. Current density of what? You do need to be more specific.

#### Oscar6330

System: Simple Parallel plate capacitor. We are changing the distance between the plates.

Dimension: Let A=w h, distance between plates r

Change: The distance being changed is very fast.

#### Phrak

What material is between the plates? Does current enter the plates? If so where? Is it in a circuit? You will have to do much better to get more answers.

$$C = \epsilon_r \epsilon_0 \frac{wh}{r} ,$$

where r << w, r << h

#### Oscar6330

can you eliminate "r" from the equation, since r is changing and replace it with one of the following variables

electric potential V

Total flux density B

Total Field Intensity H

Current Density J

Inductance.

#### Phrak

can you eliminate "r" from the equation, since r is changing and replace it with one of the following variables

electric potential V

Total flux density B

Total Field Intensity H

Current Density J

Inductance.
No. Im tired of guessing games.

#### quZz

Could someone explain to me what B, H, J and "changing r" have to do with capacitance? %/ Calculating capacitance is an electrostatic problem... isn't it?

#### amala_jose

i=nFj

i --> current density
nF--> charge transferrred(coulombs /mol)
j--->flux of reactant per unit area(mol/s cm2)

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