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What is the total charge inside
Solution
a)
as the charge density = p
let the electric field is E
for r < R1
Using Gauss law
p * (4pi/3) * r^3/epsilon_0 = E * 4pi * r^2
solving for E
E = p*r/(epsilon_0*3)
the electric field is p*r/(epsilon_0*3)
b) total charge on the inside surface = - total charge inside
total charge on the inside surface = - (4/3) pi * R1^3 * p
the total charge on the inside surface is - (4/3) pi * R1^3 * p

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