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A conducting spherical shell has an inner radius R;¡ and an outer radius Ro. 1) A charge Q is placed on the shell. Calculate the electric field E(r): a) for r> R. b) for R;

A conducting spherical shell has an inner radius R;¡ and an outer radius Ro. 1) A charge Q is placed on the shell. Calculate the electric field E(r): a) for r> R. b) for R;

Question
A conducting spherical shell has an inner radius Rj and an outer radius Ro. 1) A charge Q is placed on the shell. Calculate the electric field E(r): a) for r> R. b) for R;<r< Ro c) for r< Rj. d) Plot E(r) versus r. Ro Ri
Transcribed Image Text:A conducting spherical shell has an inner radius Rj and an outer radius Ro. 1) A charge Q is placed on the shell. Calculate the electric field E(r): a) for r> R. b) for R;<r< Ro c) for r< Rj. d) Plot E(r) versus r. Ro Ri
Expert Solution
Step 1

Given,

the total charge on the spherical shell is Q

The inner radius of the shell is Ri

The outer radius of the shell is Ro

 

Then charge density will be

ρ=QV=Q43πRo3-43πRi3=3Q4πRo3-Ri3

 

And according to gauss law, the electric flux passing through any closed surface is 1εo (for air medium) times the charge enclosed inside the surface. That is

ϕ=Qenεo

And flux can be written in terms of the electric field as

ϕ=∮E→.ds→

Then

∮E→.ds→=Qenεo

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