Electric field at a distance greater than the radius of sphere

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SUMMARY

The electric field E(r) at a distance r greater than the radius rb of a uniformly charged solid ball is derived using the formula E(r) = (Q/ε) * (1/Area). The charge Q is calculated as Q = ρ * V, where V is the volume of the sphere, specifically V = (4/3)πrb³. The correct expression for the electric field outside the sphere is E(r) = (ρ * (4/3)πrb³) / (ε * 4πr²), simplifying to E(r) = (ρrb³) / (3εr²). This highlights the importance of correctly identifying the area used in the calculations.

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Homework Statement



A solid ball of radius rb has a uniform charge density ρ.

What is the magnitude of the electric field E(r) at a distance r>r_b from the center of the ball?

Homework Equations



E(r) = (Q/ε)*1/Area

The Attempt at a Solution



If Q=ρrb

and Area = (4/3)πr3,

then E(r) = \frac{ρr<sub>b</sub>}{ε*(4/3)*πr<sup>3</sup>}


However,
the correct answer is in the image attached.
E(r)=
=%5Cfrac%7B%7B%5Crho%7D+%7Br_%7Bb%7D%7D%5E%7B3%7D%7D%7B3+%7B%5Cepsilon%7D_%7B0%7D+r%5E%7B2%7D%7D.gif

 
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Area is not (4/3) pi r^3

Also, Idon't think q = prb
 
Oh. I get it now. Thanks!
 

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