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Introductory Physics Homework Help
Calculus to calculate charge
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[QUOTE="kbwelch17, post: 4508871, member: 488427"] [h2]Homework Statement [/h2] A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r) = ρ0(1-r/R) for r≤R ρ(r) = 0 for r≥R where ρ0 = 3Q/∏R^3 is a positive constant. (a.) Show that the total charge contained in the charge distribution is Q. (b.) Show that the electric field in the region r≥R is identical to that produced by a point charge Q at r = 0. (c.) Obtain an expression for the electric field in the region r≤R. (d) Graph the electric field magnitude E as a function of r. (e.) Find the value of r at which the electric field is maximum, and find the value of that maximum field. [h2]Homework Equations[/h2] Gauss' Law : Flux = ∫E dot dA = Qencl/ε 0 Electric Field of a point charge: E = k*(q/r^2) [h2]The Attempt at a Solution[/h2] I am really just having trouble setting up the integral. You would be integrating the electric field over a sphere, so you would need to choose dA (is this a slice of the area of the sphere?) and a formula to find electric field for a given r. In order to find the latter you would need to use Gauss' Law in which case a give r would give the electric field ρ(r) = q /A1 (is this the area or the volume of the sphere in question?) q = ρ(r)*A1 E*A2 (what area is this?)= q/ε0 E = ρ(r)*A1 / A2*ε0 There are a few things I am confused about in here so please feel free to ask me to clarify anything. I need to know if I am on the right track here. Thanks! [/QUOTE]
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