Register to reply

Dielectric sphere in constant E-field

by sunrah
Tags: constant, dielectric, efield, sphere
Share this thread:
Jan10-12, 09:54 AM
sunrah's Avatar
P: 91
1. The problem statement, all variables and given/known data
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]

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!!
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100

Register to reply

Related Discussions
D-field -> E-field when the dielectric constant is a function of space Classical Physics 0
Dielectric sphere in point charge electric field Classical Physics 5
Electric Field of a Dielectric Sphere Introductory Physics Homework 3
Electric Field inside and outside of Dielectric sphere Introductory Physics Homework 0
Dielectric Sphere in Field of a Point Charge Advanced Physics Homework 1