Guass Law

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Homework Statement



I. A non-conducting sphere of radius a has a spherically symmetric, but non-uniform charge distribution is placed on it, given by the volume density function: p(r) = C·r, where C is a positive constant, and 0 < r < a.

a. Find an algebraic expression for the total charge Q on the sphere, in terms of the parameters C and a.

II. Use Gauss' Law to find an algebraic expression for the magnitude of the electric field at a distance R from the origin, in each of the following regions. Express your answer in terms of the following four parameters: the electrostatic constant k; the radius a of the sphere; the total charge Q on the sphere; and the radial distance R from the origin to the field point.

b. Within the insulating sphere (i.e. for R <a):

c. Outside the sphere (i.e. for R > a):



The Attempt at a Solution



I got Q = Cpi(a^4) for part a which is correct.


For part 2 I am stuck both b and c.

I got [(KQR^4)/((a^4)(r^2))] which is incorrect.
 

Answers and Replies

  • #2
ehild
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For part 2 I am stuck both b and c.

I got [(KQR^4)/((a^4)(r^2))] which is incorrect.
Is this your answer for b) or c)? What is r in your formula?

ehild
 
  • #3
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r is what I got with determining K. I got [tex]\frac{1}{4\pi \epsilon_0 r^2},[/tex] but I replaced the 1/4pi e_0 with K.
 
  • #4
vela
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What does ##r## represent physically? ##R## is the distance from the center of the sphere; ##a## is the radius of the sphere. What is ##r##?

You need to show your work. Just posting an incorrect answer is next to useless for us to see where you're getting stuck.
 

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