Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Engineering and Comp Sci Homework Help
Gauss' Law, Spherical Charge Distribution
Reply to thread
Message
[QUOTE="Fronzbot, post: 2902760, member: 221907"] Before I get into the question I'd just like to state that this is not homework, but questions in my book that I'm going through to prepare myself for the midterm in one week. I got stuck at a few questions, here's the first one. I won't ask the next until I'm done with this and so forth. Normally I'd go to my professor for help but I can literally not understand him when he speaks. It's awful. Luckily he's a lenient grader (at least compared to other EM Fields profs), but yeah. Ok, onto the question then... [h2]Homework Statement [/h2] A spherical distribution of charge [tex]\rho = \rho_{0}[1-(R^{2}/b^{2}][/tex] exists in the region [tex]0\leqR\leqb[/tex]. This charge distribution is concentrically surrounded by a conducting shell with inner radius [tex]R_{i} (>b)[/tex] and outer radius [tex]R_{o}[/tex]. Determine [b]E[/b] everywhere. [h2]Homework Equations[/h2] [tex] \int E \cdot ds = Q_{enc} / \epsilon_{0} [/tex] [h2]The Attempt at a Solution[/h2] I have the right answers (from the back of the book) but cannot figure out how to get there. Before I write my solution down, here are the correct answers: [tex] For 0 \leq R \leq b:[/tex] [tex] E_{R1} = \frac{\rho_{0}R}{\epsilon_{0}}(\frac{1}{3}-\frac{R^{2}}{5b^{2}}) [/tex] [tex] For b \leq R < R_{i}: [/tex] [tex] E_{R2} = \frac{2 \rho_{0} b^{3}}{15 \epsilon_{0} R^{2}} [/tex] [tex] For R_{i}<R<R_{o} [/tex] [tex] E_{R3} = 0 [/tex] [tex] For R > R_{o}: [/tex] [tex] E_{R4} = \frac{2 \rho_{0} b^{3}}{15 \epsilon_{0}R^{2}} [/tex] Now I didn't get very far, but here's what I have: [tex] Q_{enc} = \int \rho dV = \rho_{0}[1 - \frac{R^2}{b^2}]\frac{4\pi R^{3}}{3} [/tex] [tex] \int E \cdot ds = E_{R1} 4 \pi R^{2}[/tex] [tex] E_{R1} = \frac{\rho [1-\frac{R^2}{b^2}]R}{3\epsilon_{0}}[/tex] [tex] E_{R1} = \frac{\rho R}{\epsilon}(\frac{1}{3}-\frac{R^2}{3b^2}) [/tex] I have some work for the next two, but I'd rather go one step at a time here to make sure I completely what's going on. At least this answer is close, but I'm not sure where the book's 5b^2 came from. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Engineering and Comp Sci Homework Help
Gauss' Law, Spherical Charge Distribution
Back
Top