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Introductory Physics Homework Help
Flux Through a Non-Concentric Sphere
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[QUOTE="collinsmark, post: 4959580, member: 114325"] Allow me to follow up with an exercise for you. If you can successfully complete this exercise, you should have a firm grasp of Gauss' Law, flux, and what it all really means. In Figure 1a I drew a point charge surrounded by a spherical, Gaussian surface. I actually drew it as a two-dimensional circle, but you can think of it as a three dimensional sphere if you wish. The diagram shows eight "lines" of electric field (eight lines of flux, if you'd rather call them that). The number of field lines is proportional to the charge. I'll quantify the charge as 8 μC. Now let's take each case, one at a time. (a) As I mentioned in my last post, the total flux is proportional to the net number of field lines leaving the surface. So how many (net) lines of electric field (lines of flux) leave the surface? So what is the total flux? [Hint: Each line of electric field in this case corresponds to (1 μC)/[I]ε[/I][SUB]0[/SUB] of flux.] (b) What if we change the size of the sphere? Recall that the surface area of a sphere is proportional to [I]r[/I][SUP]2[/SUP]. Also recall that the electric field is proportional to 1/[I]r[/I][SUP]2[/SUP]. Find the flux in this case. (Hint: So once again it all comes down to the net number of electric field lines/flux lines leaving the surface.) (c) What if the charge is no longer in the center of the sphere? Calculate the number of lines leaving the surface and calculate the corresponding total flux. (d) Now calculate the total (net) flux if instead of a spherical surface, we use an arbitrarily shaped, closed surface. Don't forget that if a line leaves the surface it counts as a positive amount of flux, and if it enters the surface it counts as a negative. A given line may leave and/or enter the surface more than once. Your goal is to find the [I]net[/I] number of lines exiting the surface, and the corresponding total, net flux. (e) What if we move the charge outside the sphere? Find the total amount of (net) flux leaving the surface in this case. (f) Same as above except with an arbitrarily shaped, closed surface. [ATTACH=full]77040[/ATTACH] Figure 1. [/QUOTE]
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Flux Through a Non-Concentric Sphere
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