Suppose the charge density inside a plastic sphere isnon-uniform and given by =r

Question

Suppose the charge density inside a plastic sphere isnon-uniform and given by =r5+. and are constants. What is the electric field as a functionof r inside the sphere? Don't really know where to go with this problem, never wentover it in class and can't find help in the text book. Help? Suppose the charge density inside a plastic sphere isnon-uniform and given by =r5+. and are constants. What is the electric field as a functionof r inside the sphere? Don't really know where to go with this problem, never wentover it in class and can't find help in the text book. Help?

Explanation / Answer

How will you know if it "looks right"? Trust me, it will beright. I don't care how you think it "looks". . Jeeezus... . Anyway... Gauss' Law .    integral of E dA = charge enclosed .    E 4r2   =    integral of (densitydV)           where dV is a spherical shell... so dV = 4r2dr . E 4 r2  =    integral of [ (r5 + ) (4 r2 dr) ]    from r = 0 to r . E 4 r2  =    4   integral of  (r7   + r2)dr . E r2  =    (1/8) r8  +   (1/3) r3 .       E = (1/) [ (1/8) r6  + (1/3) r ]

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