Gauss' law for charge distribution of a point charge at the origin surrounded by an insulating sphere

AI Thread Summary
The discussion revolves around applying Gauss' law to a point charge at the origin within an insulating sphere. The electric field is non-zero in the region from 0 to R1 due to the point charge Q. For the region beyond R2, it is necessary to perform an integral to determine the total charge on the sphere, which, when added to the charge at the origin, provides the enclosed charge. The original poster seeks validation for their approach and methods to verify their solution. Understanding these principles is essential for accurately solving problems involving charge distributions.
BlondEgg
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Homework Statement
Use Gauss law for sphere
Relevant Equations
Gauss law
Hi

I'm trying to solve this

1721256051554.png


So far I have got
1721256094639.png


1721256118187.png

But me not sure whether it correct or not. Maybe someone knows of a way you can check answer is correct like in math when you plug solution to solve equation?

Best wishes to you
 
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In the first region ##0 \leq r \leq R_1## the electric field is not zero. The problem clearly states that there is point charge ##Q## at the origin.

Also, in the region ##r>R_2## you need to do the integral to find the total charge on the sphere. That, plus the charge at the origin should give you the enclosed charge.
 

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