GREPhysics.NET: GR8677 #80

GR8677 #80

Problem

GREPhysics.NET Official Solution

Electromagnetism $\Rightarrow$ }Gauss Law

Recall the differential form of Gauss' Law $\nabla \cdot \vec{E}=\rho$ . For fields that contain no charges, the equation becomes $\nabla \cdot \vec{E}=0$ . Find the choice with 0 divergence.

(A) $A(2y-x) \neq 0$

(B) $A(-x+x)=0$ ... so this is it!

(C) $A(z) \neq 0$

(D) $A(yz+xz) \neq 0$

(E) $Ayz \neq 0$

Alternate Solutions

casseverhart13 2019-08-23 12:20:38	I really appreciate this problem....thanks.... tree service Orlando Reply to this comment
nakib 2010-04-02 09:01:27	Don't go for calculating all the answer choices for $\nabla\cdot E = 0$ . Eliminate C, D ~> Each term has a non-zero contribution to the div. but both terms are +ve, they can't possible cancel each other out. Eliminate E ~> Just one term that has a non-zero contribution to the div. Eliminate A ~> Each term has a non-zero contribution to the div. but one term has a factor of $2$ multiplied to it. (B) is the correct choice. Reply to this comment
senatez 2006-10-16 20:25:28	The electric field must also be a gradient of a function (the potential). Mixed partials of the potential function must be equal. Reply to this comment

Comments

casseverhart13
2019-08-23 12:20:38

I really appreciate this problem....thanks.... tree service Orlando

Reply to this comment

nakib
2010-04-02 09:01:27

Don't go for calculating all the answer choices for $\nabla\cdot E = 0$ .

Eliminate C, D ~> Each term has a non-zero contribution to the div. but both terms are +ve, they can't possible cancel each other out.

Eliminate E ~> Just one term that has a non-zero contribution to the div.

Eliminate A ~> Each term has a non-zero contribution to the div. but one term has a factor of $2$ multiplied to it.

(B) is the correct choice.

neon37
2010-11-04 04:40:24

Its not too hard if you think about how to do it fast before hand. It might take longer to think about some other logic. Divergence is a dot product, so for $\hat{e_i}$ terms you take $\frac{\partial}{\partial x_i}$ . That shouldnt be too difficult. In this case it was just the second one, so it took me about 7 seconds maximum after reading the question.

Reply to this comment

senatez
2006-10-16 20:25:28

The electric field must also be a gradient of a function (the potential). Mixed partials of the potential function must be equal.

student2008
2008-10-12 12:08:08

Not necessarily. Since $\vec E = -\frac1c \frac{\partial\vec A}{\partial t} -\nabla \phi$ , you're right only in the electrostatic case, which takes place here. And in general we can't get rid of the $\frac{\partial \vec A}{\partial t}$ by a gauge transformation, since the condition $\frac{\partial \vec A}{\partial t}=0$ implies ${\bf three}$ scalar ones.

Although, since there're only ${\bf static}$ expressions for the electric field, we can infer that the problem ${\bf is}$ electrostatic.

Prologue
2009-11-06 21:03:53

You can't infer that it is electrostatic, the curl is nonzero.

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...

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