- #1

happyparticle

- 442

- 20

- 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?