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Electric Field of a Spherical Shell
 Electric Field of Two Spherical shells
 Uniformed Charged Solid Sphere
 Source and Reference

Electric Field of a Spherical Shell

image 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=14πœ‹πœ€0𝑄|π‘Ÿ|2π‘Ÿ for π‘Ÿ>𝑅
𝐸=0 for π‘Ÿ<𝑅

Electric Field of Two Spherical shells

image The electric field 𝐸 of two concentric spherical shell of the same charges 𝑄. 𝐸=14πœ‹πœ€02𝑄|π‘Ÿ|2π‘Ÿ for π‘Ÿ>b
𝐸=14πœ‹πœ€0𝑄|π‘Ÿ|2π‘Ÿ for b>π‘Ÿ>a
𝐸=0 for π‘Ÿ<a

Uniformed Charged Solid Sphere

image The uniformly charged solid sphere of radius 𝑅 is Total Charge: 𝑄; Total Volume: 𝑉=43πœ‹π‘…3
Charge per unit volume=𝑄(4/3)πœ‹π‘…3
The charged partial solid sphere of radius π‘Ÿ is Total Charge: βˆ†π‘ž; Total Volume: βˆ†π‘‰=43πœ‹π‘Ÿ3
Charge per unit volume=βˆ†π‘ž(4/3)πœ‹π‘Ÿ3
If uniform distributed charge 𝑄(4/3)πœ‹π‘…3=βˆ†π‘ž(4/3)πœ‹π‘Ÿ3β‡’βˆ†π‘ž=π‘„π‘Ÿ3𝑅3 The outside electric field of partial solid sphere of radius π‘Ÿ can be expressed as πΈπ‘Ÿ=14πœ‹πœ€0βˆ†π‘žπ‘Ÿ2π‘Ÿ
𝐸(π‘Ÿ)=14πœ‹πœ€0π‘„π‘Ÿ3𝑅3π‘Ÿ2
 
π‘Ÿ=𝑄4πœ‹πœ€0π‘Ÿπ‘…3π‘Ÿ for π‘Ÿ<𝑅

Source and Reference

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


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ID: 191102502 Last Updated: 11/25/2019 Revision: 0


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