 #1
happyparticle
 371
 19
 Homework Statement:

Find the Boundary conditions for (E and D) for a dielectric sphere.
##\vec{P} = P\hat{z}##
 Relevant Equations:
 ##\sigma_b = \vec{P} \cdot \hat{n}##
Since there is no free charge ##\int_S \vec{D} \cdot d\vec{a} = 0## and
##\rho_f = 0##
##\sigma_f = 0##
##\vec{nabla} \cdot \vec{P} = 0## since P is a constant
##\rho_b =  \vec{nabla} \cdot \vec{P} = 0##
For a simple surface we can find the boundary conditions for ##\vec{E}## using a Gauss' surface to verify ##E^{\perp}_{above}  E^{\perp}_{below}## and ##E^{}_{above}  E^{}_{below}##
However, how to verify the boundary conditions for a sphere?
##\rho_f = 0##
##\sigma_f = 0##
##\vec{nabla} \cdot \vec{P} = 0## since P is a constant
##\rho_b =  \vec{nabla} \cdot \vec{P} = 0##
For a simple surface we can find the boundary conditions for ##\vec{E}## using a Gauss' surface to verify ##E^{\perp}_{above}  E^{\perp}_{below}## and ##E^{}_{above}  E^{}_{below}##
However, how to verify the boundary conditions for a sphere?