Electric Field of a Spherical Shell

The electric field 𝐸 has same symmetries as the sphere. And far away, looks like a point charge. In other words, the form of electric field must have the form similarly. 𝐸=14𝜋𝜀0𝑄|𝑟|2𝑟 for 𝑟>𝑅
𝐸=0 for 𝑟<𝑅

Electric Field of Two Spherical shells

The electric field 𝐸 of two concentric spherical shell of the same charges 𝑄. 𝐸=14𝜋𝜀02𝑄|𝑟|2𝑟 for 𝑟>b
𝐸=14𝜋𝜀0𝑄|𝑟|2𝑟 for b>𝑟>a
𝐸=0 for 𝑟<a

Uniformed Charged Solid Sphere

The uniformly charged solid sphere of radius 𝑅 is Total Charge: 𝑄; Total Volume: 𝑉=43𝜋𝑅3
Charge per unit volume=𝑄(4/3)𝜋𝑅3 The charged partial solid sphere of radius 𝑟 is Total Charge: ∆𝑞; Total Volume: ∆𝑉=43𝜋𝑟3
Charge per unit volume=∆𝑞(4/3)𝜋𝑟3 If uniform distributed charge 𝑄(4/3)𝜋𝑅3=∆𝑞(4/3)𝜋𝑟3⇒∆𝑞=𝑄𝑟3𝑅3 The outside electric field of partial solid sphere of radius 𝑟 can be expressed as 𝐸𝑟=14𝜋𝜀0∆𝑞𝑟2𝑟
𝐸(𝑟)=14𝜋𝜀0𝑄𝑟3𝑅3𝑟2
 𝑟=𝑄4𝜋𝜀0𝑟𝑅3𝑟 for 𝑟<𝑅

Source and Reference

https://www.youtube.com/watch?v=6-DKowkyBmQ&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=7