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Homework Statement
Consider a spherical dielectric shell so that ε = ε_0ε_r for a < r < b and ε = ε_0 for 0 < r < a. If a charge Q is placed at the center of the shell, find
a) P for a < r < b
b) ρ_pv for a < r b
c) ρ_ps at r = a and r = b
Homework Equations
ρ_pv = -div(P)
ρ_ps = P [itex]\cdot[/itex]a_n
The Attempt at a Solution
I've managed to solve a) with the answer
Q/(4*pi*r^2) * (ε_r-1)/ε_r
which is correct (checked the answers).I've also solved b) which is ρ_pv = 0 since ρ_pv = -div(P).
I have trouble to find ρ_ps at r = a and r = b. The answer states that
-Q/(4*pi*a^2) * (ε_r-1)/ε_r and -Q/(4*pi*b^2) * (ε_r-1)/ε_r
respectively. Where is that negative sign coming from?