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I have a series of questions on a basic charged sphere and deriving quantities such as the infinitesimal charge, the total charge and the electric field. The question is part (b) in the image below:

So I found [tex]dQ'[/tex] by equating it to the surface area of a shell at a distance [tex]r'[/tex] multiplied by the corresponding charge density to attain:

[tex]dQ'=\frac{4\pi \rho _{0}r'^6dr'}{R^4}[/tex]

Is this right?

And then for the next part I just integrated over r' for some r'<R to attain:

[tex]Q=\frac{4\pi\rho _{0}r'^7}{7R^4}[/tex]

and then the last part I wish to query is my electric field magnitude, which I attained from equating the product of the electric field and area of some shell at distance r' to the charge divided by the permitivitty of free space to attain:

[tex]E=\frac{\rho _{0}r'^5}{7R^4\epsilon _{0}}[/tex]

Is this right?

Thanks guys!

Any feedback appreciated,

SK

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# Homework Help: Electromagnetism Charged Sphere Q.

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