# displacement current - electrodynamcis

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 November 11, 2011, 06:48 displacement current - electrodynamcis #1 New Member   Christian Jungreuthmayer Join Date: Mar 2009 Posts: 9 Rep Power: 17 Hi Foamers, I just wonder if someone of you has already developed a transient solver that can calculate the ohmic and displacement current, e.g. in a parallel-plate capacitor with a dielectric material that has an electric conductivity > 0. In other words, I would like to solve an equation looking like this: div(J) = 0, where J is the electric current density [A/m2] which is given by J = J_ohmic + J_displacement J = sigma*E + d(D)/dt, where sigma is the electric conductivity [S/m], E the electric field strength [V/m], and D the electric flux density [As/m2] which is differentiated by the time t [s]. The electric flux density D is given by D = epsilon*E, where epsilon is the permittivity in [F/m]. As the electric field strength E can be determined using the electric potential V (E= -grad(V)) the entire equation to be solved can be expressed as: div( sigma*grad(V) + d(epsilon*grad(V))/dt ) = 0 I was spending quite some time trying to develop a solver that can do that. Unfortunately, without success. The time derivative inside the divergence operation is giving me a hard time. Any help would be very appreciated. Cheers, Christian

 Tags capacitor, displacement current, electrodynamics, parallel-plate