- #1
sunrah
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Homework Statement
Given a dielectric sphere with relative permittivity = ε in a homogeneous E-field:
[itex]\vec{E_{0}} = E \vec{e_{z}}[/itex].
The E-field causes a homogeneous polarisation (dipole density) of
[itex]\vec{p} = \frac{vec{P}}{V} [/itex] with big P the dipole moment vector. The total electric field outside is:
[itex]\vec{E^{ex}} = \vec{E_{0} - \frac{1}{4 \pi \epsilon_{0}} ( \frac{\vec{P}{r^{3}} - \frac{\vec{3P}{r^{5}}} ) [/itex]
Question: Use the continuous nature of the normal component of [itex]\vec{D}[/itex] at the surface to show that:
[itex]\epsilon_{0} E^{in} = E_{0} + \frac{2P}{4\pi\epsilon_{0}}[/itex]
Homework Equations
Using [itex]\vec{D^{ex}_{n}} = \vec{D^{in}_{n}}[/itex] , e.g. normal component of D is continuous at surface
and [itex]\vec{\frac{D^{ex}_{t}}{\epsilon_{0}}} = \vec{D^{in}_{t}}[/itex]
The Attempt at a Solution
I simply don't know what to do I've messed around with this and got nowhere. Please help!
Latex isn't rendering properly - vector arrows are appearing as small boxes but please try and help!
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