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Dielectric sphere in constant Efield 
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#1
Jan1012, 09:54 AM

P: 91

1. The problem statement, all variables and given/known data
Given a dielectric sphere with relative permittivity = ε in a homogeneous Efield: [itex]\vec{E_{0}} = E \vec{e_{z}}[/itex]. The Efield 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] 2. Relevant 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] 3. 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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