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3. A non-conducting sphere (R-0.05 m) is charged with a non-uniform charge density pr)-(0.64 a)-~ 0.2037:r (in units of Cim3). For a variable distance rin from the center within the sphere, integrate da p(r)-dV from the center (r 0) out to rin to find the charge qemerin) contained within the radius rin R. [reminder: the differential volume of a thin shell is dV= 4nr2dr Evaluate qen at r,-R to find the total charge Qo on the sphere. ( At a specific radius r 2.5 em what is the electric field E(m) within the sphere? Km Finally, at a radius rout-1 m outside the sphere what is the electric field E(^ou)? Tin en(in) da on shell)

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3 E.ds 4TT 1)2

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