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Located at the centre of a symmetric dielectric shell (spherical, of radius ri​ and outer radius r0​ ) is a symmetric free charge (density Pfree ​ ). The dielectric constant is Epsilon =1+x - Use the following equation to find the magnitude of the displacement field: D=4πr2Qfree ​​ - Find the relationship between Pfree ​ and Qfree ​ - Using what is found between the electric and displacement field, find the electric field at radius r inside the dielectric shell (r1r2). At r>r2, how is the continuity of the displacement field across the surface of the shell?

Answer :

The relationship between Pree ​ and Q free ​ is given by the equation Q

free = P free V,

where V is the volume of the symmetric charge.

By substituting P free​ into the equation of electric field

E= q/epsilon,

we get.

E= Q free/ (4πr²epsilon) for rr2,

E is given by

E = Q free / (4πepsilonr²)

Epsilon, since the dielectric constant is given by

epsilon= 1+x.

E > Epsilon for r>r2.

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