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Charge and current density

  1. Mar 24, 2009 #1
    Can we make a mathematical (equation) relationship between Current Density and Charge Q.
     
  2. jcsd
  3. Mar 25, 2009 #2
    hmm... it seems to me that without any additional information it is only possible to connect dQ/dt with j.
     
  4. Mar 25, 2009 #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.
     
  5. Mar 25, 2009 #4
    There is a relationship between charge density and current density; the charge continuity equation.
     
  6. Mar 25, 2009 #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...
     
  7. Mar 25, 2009 #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.
     
  8. Mar 25, 2009 #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
     
  9. Mar 25, 2009 #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? =)
     
  10. Mar 25, 2009 #9
    LOL....well since this is not an assignment, so no one has solved it. So the problem still remains unsolved
     
  11. Mar 25, 2009 #10
    It's a relativistic equation as well. The charge continuity equation is Lorentz invariant, and more, is covariant without connections on a curved spacetime.
     
  12. Mar 25, 2009 #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.
     
  13. Mar 26, 2009 #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.
     
  14. Mar 26, 2009 #13
    To be honest, I cannot understand where its going. Can you guys please redirect to my topic
     
  15. Mar 26, 2009 #14
    you are right. the relativistic interpretation of the charge density as a probability can be the object of another topic.
     
  16. Mar 26, 2009 #15
    Sure, Oscar. Without a little more to go on, we don't know what to go on. You need to explain your system.
     
  17. Mar 26, 2009 #16
    That sounds interesting. Why don't you start a thread?
     
  18. Mar 26, 2009 #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)
     
  19. Mar 26, 2009 #18
    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.
     
  20. Mar 26, 2009 #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.
     
  21. Mar 27, 2009 #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
     
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