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

[BlondEgg]

Homework Statement

Use Gauss law for sphere

Relevant Equations

Gauss law

Hi

I'm trying to solve this

So far I have got

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

 

[kuruman]

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.