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# Polarisation of surface of a hollow sphere??? HEEEELP?? watch

1. Hi physicists,

Quick 2 marker for you to help me with please! :]

I have an expression for the vector of polarisation of the surface of a hollow sphere. The question then asks: 'What is the total charge required within the volume to ensure no net charge?'

I know I will probably have to integrate something, but I have no idea apart from that.

Thanks
2. if vector of polarisation is what i think it is then...

the charge density will be like P.n where n is normal to the surface,

Spoiler:
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so integrate P.n over the sphere's surface

and then that gives the charge on the surface, so need negative of that inside
3. The charge on the surface, Q = -integral (P.dA).
Using the divergence theorem, you can convert the RHS into a volume integral. Then you have Q = -integral (del.P)dV.
So just calculate del.P and then integrate over the volume of the sphere to get the charge on the surface.
The total charge inside the volume of the sphere will have the same magnitude but opposite sign.

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