GREPhysics.NET: GR8677 #10

GR8677 #10

Problem

GREPhysics.NET Official Solution

Electromagnetism $\Rightarrow$ }Gauss' Law

Only choices C, D, and E make sense, since the field at $r=0$ has to be 0. Moreover, since a uniform charge distribution is applied, the field has to increases linearly within the volume of the sphere. Choice D and E are both out, leaving just C.

Direct verification via applying Gauss' Law for the inside of the sphere: $E(4\pi r^2)=Q=\rho \frac{4}{3}\pi r^3\Rightarrow E=\frac{\rho r}{3}\propto k r$ .

Outside, all five choices converge to an inverse-square decreasing field---so, no worry there!

Alternate Solutions

There are no Alternate Solutions for this problem. Be the first to post one!

Comments

nmast
2009-11-24 09:16:37

Since the charge density is uniform, shouldn't E go like Q enclosed? Being a sphere, this would be like r^3, making D correct.

kroner
2009-11-27 19:08:54

No. Q is proportional to $r^3$ , but E is proportional to $Q/r^2$ which means E is linear in r, as in choice C.

Reply to this comment

wittensdog
2009-09-24 21:45:16

ETS sure does love to throw in unnecessary details - who cares if the charge is positive or negative when it comes to the field magnitude?

Reply to this comment

Andresito
2006-03-14 22:37:41

Gauss' law E*A = Q/epsilon

Yours is an approximation.

Thanks Yosun.

lxanderl
2009-06-28 17:23:43

Depends on if he's using cgs or SI

Reply to this comment

Post A Comment!

Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...

<a href="http://www6.shoutmix.com/?grephysics">View shoutbox</a>
ShoutMix chat widget

Free 3D Virtual World. Largest User-Created Fantasy World. Don't Play, Experience. Join Now!

Bored, got time to kill, and want to earn micro-cash by mindlessly clicking on links? Join CrownGPT. Click Offers. Click the Paid to Click button... then click to your heart's delight.

FREE 3D Virtual World Chat - Join Second Life Today!

All-Solutions List | Latest Comments | Unanswered Questions (Cries for Help!) |::| About

This site is not affiliated with ETS, nor is it officially endorsed (yet) by ETS. This site is the work of an individual named Yosun Chang. The solutions, sans user comments and ETS questions, are © 2005 by Yosun Chang except where noted. All rights reserved. / The comments appending particular solutions are due to the respective users. / Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 1997 and © 2001 by ETS.

Bare Basic LaTeX Rosetta Stone