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gerryliyana
 2 years ago
Partial Differential Problem
gerryliyana
 2 years ago
Partial Differential Problem

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gerryliyana
 2 years ago
Best ResponseYou've already chosen the best response.0Assume from electricity the equations \(\nabla . \bar D = \rho \) (\(\bar D \) = electric displacement ) and \(\rho \) = charge density and \(\bar D =  \epsilon \nabla \phi \), \(\phi \) = electrostatic potential and \(\epsilon\) = dielectric constant. Show that the electric potential satisfies laplace's equations in a charge free region and satisfies poisson's equation in a region of charge density \(\rho\).

gerryliyana
 2 years ago
Best ResponseYou've already chosen the best response.0i typed, have idea, @rox13kh ???

gerryliyana
 2 years ago
Best ResponseYou've already chosen the best response.0hei where are you going @rox13kh ??

gerryliyana
 2 years ago
Best ResponseYou've already chosen the best response.0@UnkleRhaukus @oldrin.bataku have idea ??

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.3in a chargefree region \(\rho=0\) and u have\[\nabla . \bar D = \rho=0\]and we know \(\bar D =  \epsilon \nabla \phi\) so\[\nabla . ( \epsilon \nabla \phi)=0\]\[\nabla . ( \nabla \phi)=0\]\[\nabla^2 \phi=0 \ \ \ \ \color\red{\text{Laplace Equation}}\]

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.3in a similar process\[\nabla . ( \epsilon \nabla \phi)=\rho\] in a region of charge density \(\rho\) . if \(\epsilon\) is constant\[\epsilon \ \nabla^2 \phi=\rho \ \ \ \ \color\Green{\text{ Poisson's Equation}}\]

gerryliyana
 2 years ago
Best ResponseYou've already chosen the best response.0ah thank you @mukushla ..., i have another one .., wanna help me again?
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