- #1

sliperyfrog

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## Homework Statement

A non-conducting sphere of radius

**a**carries a non-uniform charge density. The electrostatic field inside the sphere is a distance

**b**from is center and is given by

**E = (b/a)**(

^{4}E_{0}**E**being the maximum magnitude of the field.)

_{0}a. Find an expression for

**E**in terms of the total charge

_{0}**Q**and the radius of the sphere.

_{0}b. Determine the charge density of the sphere as a function of radius.

## Homework Equations

ε

_{0}∫ E ⋅ dA = ∫ ρdV

dQ = ρdV[/B]

## The Attempt at a Solution

[/B]

So for a I did

**ε**since

_{0}∫ E ⋅ dA = ε_{0}E4πa^{2}

E = (b/a)

ε

E = (b/a)

^{4}E_{0}ε

_{0}E4πa^{2}=**ε**

_{0}(b/a)^{4}E_{0})4πa^{2}= 4πE_{0}ε_{0}(b^{4}/a^{2})For the

**∫ ρdV**side of the problem my professor did it a problem similar in his slides for

**b > a**of uniform charge density the

**∫ ρdV = Q**so i just assume it is the same for a non-uniform charge density. Getting me

_{0}**4πE**

thus

_{0}ε_{0}(b^{4}/a^{2}) = Q_{0}**E**

_{0}= (a^{2}Q_{0})/(4πb^{4})For part b I did

**dQ**so

_{0}= ρdV = ρ4πa^{2}da**Q**so

_{0}= ∫_{0}^{b}ρ4πa^{2}da = (4/3)πρb^3**ρ = (3Q**

_{0})/(4πb^{3})