Charge and current density

In summary, the conversation discusses the possibility of making a mathematical relationship between current density and charge Q in a given system. The system in question is a parallel plate capacitor with changing distance between the plates. The available outputs from the simulation software are electric potential U, total flux density D, total field intensity E, current density J, and inductance. The equation C=Q/V is mentioned, along with the continuity equation and the possibility of a relativistic interpretation of charge density. However, there is a lack of specific information about the system and its dimensions, leading to an inability to provide a specific equation for capacitance. The conversation also briefly touches on the relationship between current density and charge transfer in a chemical reaction.
  • #1
Oscar6330
29
0
Can we make a mathematical (equation) relationship between Current Density and Charge Q.
 
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  • #2
hmm... it seems to me that without any additional information it is only possible to connect dQ/dt with j.
 
  • #3
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.
 
  • #4
There is a relationship between charge density and current density; the charge continuity equation.
 
  • #5
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...
 
  • #6
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.
 
  • #7
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
 
  • #8
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? =)
 
  • #9
LOL...well since this is not an assignment, so no one has solved it. So the problem still remains unsolved
 
  • #10
naturale said:
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.
 
  • #11
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.
 
  • #12
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.
 
  • #13
To be honest, I cannot understand where its going. Can you guys please redirect to my topic
 
  • #14
you are right. the relativistic interpretation of the charge density as a probability can be the object of another topic.
 
  • #15
Oscar6330 said:
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.
 
  • #16
naturale said:
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?
 
  • #17
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)
 
  • #18
Oscar6330 said:
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.
 
  • #19
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.
 
  • #20
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.

[tex]C = \epsilon_r \epsilon_0 \frac{wh}{r} ,[/tex]

where r << w, r << h
 
  • #21
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.
 
  • #22
Oscar6330 said:
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. I am tired of guessing games.
 
  • #23
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?
 
  • #24
i=nFj

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

1. What is charge density?

Charge density refers to the amount of electric charge per unit volume in a given material or space. It is typically denoted by the symbol ρ (rho) and is measured in coulombs per cubic meter (C/m^3).

2. How is charge density related to electric fields?

Charge density and electric fields are directly related through Gauss's Law, which states that the electric flux through a closed surface is equal to the total charge enclosed by that surface. This means that a higher charge density will result in a stronger electric field.

3. What is current density?

Current density is a measure of the flow of electric charge in a given direction. It is typically denoted by the symbol J and is measured in amperes per square meter (A/m^2). It represents the amount of current per unit area and is related to charge density through the equation J = ρv, where ρ is the charge density and v is the velocity of the charge carriers.

4. How is current density related to electric current?

Current density and electric current are directly related through the cross-sectional area of the material or space in which the current is flowing. The electric current is equal to the integral of the current density over the cross-sectional area, or I = ∫J dA.

5. What factors affect charge and current density?

Charge and current density can be affected by a variety of factors, including the material's electrical properties, the presence of external electric or magnetic fields, and the movement of charge carriers within the material. Temperature, pressure, and the presence of impurities can also impact charge and current density.

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