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Homework Statement
1. In a dilectric sphere with radius a and polarization vector P= P0 r (r is the spherical radial vector) where P0>0. find D,E and the polarization charge volume density and area density.
2. A chagrge q is displaced at the centre of a hollow dilectric sphere (with a,b as its internal an outer radii), the dilectric constant e(r) depends on the radial distance, find E,D,P.
Homework Equations
Maxwell (electrostatic) Equations and boundary conditions.
The Attempt at a Solution
For 1, I found the charge densities, [tex] \rho ' =-\nabla \b{P}= -3P0[/tex] and [tex]\sigma ' = -(\b{P}_{inside \ sphere} - \b{P}_{outside \ sphere})\cdot \b{n}= P_0 a[/tex], Now I don't know how to find D and E, from the boundary conditions I know that:
div D= [tex]4\pi \rho_{free}[/tex] and that [tex]\sigma_{free} = -(\b{D}_{inside \ sphere} - \b{D}_{outside \ sphere})[/tex], and E I can find after I find D, by the fact that D=E+4pi P.
I suppose that [tex]\sigma_{free}=-\sigma '[/tex] cause the net charge is zero, and the same with volume densities, from both equations and from the symmetry of the problem (D is spherical radial) I can find D, I am not sure if this is valid.
For 2, not sure either, if I find D then E=D/e(r), and P=(e(r)-1)/4pi)E, the question is how do I find D?
Thanks in advance.
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