A parallel plate capacitor of area 60cm^2 and separation 3mm is charged initially at 90 micro coulomb. If the medium between the plates get slightly conducting and the plate loses charge initially at the rate of 2.5 *10^-8 C per sec then what is the magnetic field between the plates?


closed as off-topic by Danu, CuriousOne, John Rennie, ACuriousMind, Kyle Kanos Mar 19 '16 at 11:07

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  • $\begingroup$ Have you tried using Maxwell's equations? $\endgroup$ – CuriousOne Mar 19 '16 at 9:01
  • 2
    $\begingroup$ Hi Mayank and welcome to the Physics SE! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. $\endgroup$ – John Rennie Mar 19 '16 at 10:37
  • $\begingroup$ @CuriousOne Yes, i applied it.Since, i'm in grade 12 and i haven't much knowledge about it.But i studied it from internet.I'm confused that how do i find displacement current and actual current. $\endgroup$ – Mayank Devnani Mar 19 '16 at 11:51
  • $\begingroup$ You apply the definition for both. $\endgroup$ – CuriousOne Mar 20 '16 at 1:34
  • $\begingroup$ I do think that this question should be reopened for a grade 12 student as there is a great deal of understanding to be gained from discussing this question particularly as it can be solved by just drawing a diagram and writing a few words. $\endgroup$ – Farcher Mar 20 '16 at 13:36

The produced magnetic field will be circular in nature. You should use Ampere's Law (with Maxwell's addition) where the produced magnetic field would be due to two sources: Direct current due to free charges and Displacement Current due to a time-varying electric field.

Since this is homework problem, it is not appropriate to give you the solution in all its steps. I hope this will give you a good hint.

  • $\begingroup$ well,it's not a homework problem.I'm in grade 12 and i got this problem from a site. Only i studied is that magnetic field between plates is zero. Could you please give me more hint. $\endgroup$ – Mayank Devnani Mar 19 '16 at 5:37
  • $\begingroup$ If you are sure that the final answer is zero, then those two terms should add up to zero. I wish I had time to do it in here but I remember once I have seen this problem. It is little bit involved as you have to make use of lots of concepts in electrodynamics which makes it a good challenging question. $\endgroup$ – Benjamin Mar 19 '16 at 6:18
  • $\begingroup$ Yes, answer is indeed zero. But i have a confusion. First, i don't the how to solve this. Second, at initial state, there is a current which is maximum cuz capacitor is charged fully.So no flow of charge is there.therefore, no magnetic field is there. At final state, current is zero,in this case no flow of charge is there.Therefore, no magnetic field is there. But i don't know how to solve at instant. Can you please tell me that i'm correct or not? $\endgroup$ – Mayank Devnani Mar 19 '16 at 7:40
  • $\begingroup$ The magnetic field inside the capacitor during the discharge will not be zero; in quasistatic discharge the Biot-Savart law is applicable and there is no net contribution due to displacement currents. See the paper by A. P. French, J.R Tessman Displacement Currents and Magnetic Fields, scitation.aip.org/content/aapt/journal/ajp/31/3/10.1119/… $\endgroup$ – Ján Lalinský Mar 19 '16 at 12:08
  • $\begingroup$ @JánLalinský I cannot access the reference that you have given as I am not a member of AAPT but suspect the analysis is done for a capacitor which is discharging through a resistor outside the capacitor. So the Poynting vector is outwards from the capacitor and inwards towards the resistor indicating a flow of energy from the capacitor into the resistor. This example is different in that the energy transfer is contained within the capacitor so the Poynting vector is zero? Since there is an electric field within the capacitor this means that the magnetic field is zero? $\endgroup$ – Farcher Mar 20 '16 at 11:51

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