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Question

A charges Q is distributed uniformly within the material of a hollow sphere of inner and outer radii r1 and r2. Find the electric field at a point p a distance x away from the centre for r1<x<r2. Draw a rough graph showing the electric field as a function of x for 0<x<2r2.
1301378_d57d1af76458468e9ebd96b1b81d57b5.png

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Solution

The charge density for the spherical shell is given as:
ζ=QV

Now, volume charge density =Q43×π×(r32r31)
ζ=3Q4π(r32r31)

Again volume of sphere having radius x is given as =43πx3

Now charge eneclosed by the sphere having radius x is:
Q=(43πχ343πr31)×Q43πr3243πr31

=Q(χ3r31r32r31)

Applying Gauss;s law E×4πx2=q enclosed0

E=Q0(χ3r31r32r31)×14πχ2=Q4π0χ2(χ3r31r32r31)

1544493_1301378_ans_14b30406b0894f339e46a22a8c9c01f2.png

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