GREPhysics.NET: GR0177 #86

GR0177 #86

Problem

GREPhysics.NET Official Solution

This problem is still being typed.

Electromagnetism $\Rightarrow$ }Faraday Law

The voltage induced is equal to the change in magnetic flux $\epsilon = -\frac{\partial \Phi}{\partial t}$ , where $\Phi =\int \vec{B} \cdot d\vec{A}$ .

Noting the initial condition ( $\Phi(t=0)=0$ ), since the field and area normal are perpendicular), one finds that $B \cdot dA = B \sin(\omega t) \pi r^2$ . Thus, $d\Phi/dt = \omega B \cos(\omega t) \pi r^2$ .

Now, to find the current, one uses Ohm's Law in Faraday's Law to get $IR/N=\dot{\Phi}$ , where N is the number of turns. Thus, $I = N/R \dot{\Phi} = NB\omega / R \cos(\omega t) \pi r^2 = 15/2 \times 300/9 \cos(\omega t) \pi (1/100)^2=250E-4\cos(\omega t)$ . This is choice (E).

Alternate Solutions

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

Comments

asdfman
2009-11-02 23:47:03

it says the coil starts at $\theta = 0$ which means $\phi (0) = 0$ and therefore a $\sin$ function.

$\frac{d \phi}{d t}$ must therefore be a cosine.

Do some algebra and you realize that it'll be something like 1.5^2, so it'll have something ~2.25 or 2.5. The only answer that fits the bill is E.

Reply to this comment

theevilmachines
2009-07-12 17:58:53

I don't know about you guys, but my 0177 test doesn't have $0.025\pi\cos(\omega t)$ as an answer choice. Choice E is $25\pi\cos(\omega t)$ . Am I missing something?

theevilmachines
2009-08-24 15:31:09

Oh it says in milliamperes, not amperes.

Reply to this comment

duckduck_85
2008-11-03 22:20:12

how do you know that the resistance given in the problem isn't for the entire coil? (so that you needn't take the # of turns into account)

elzoido238
2008-11-07 19:17:30

The problem states that "...the coil resistance is 9 $\Omega$ , which I interpret as the resistance of the entire coil. Since Yosun found the flux for 1 turn of the coil, you would need to account for the number of turns in the coil by dividing the total resistance by N (if, however one found the flux for the entire coil - i.e. $\Phi$ =NB $\pi$ $r^2$ sin( $\omega$ t) - one would not need to find the resistance per turn.)
Thanks Yosun for this kick-ass site! :)

Reply to this comment

sblmstyl
2008-10-15 21:39:49

thanks yosun!

Reply to this comment

naama99
2006-11-29 21:16:46

What do you mean by \"one uses Ohm's Law in Faraday's Law"? Can you be more specific about it? It seems to me that you are taking the R given in the question and merely using it as L

Richard
2007-10-29 09:53:54

I'm pretty sure she just means,
take Ohm's law $V=IR$ and substitute the expression for the induced voltage given by Faraday's law:
$EMF=-\frac{\partial \Phi_B}{\partial t}$
Of course you need to take into account the number of turns...

Reply to this comment

radicaltyro
2006-10-28 21:53:31

You are missing the $\pi$ in your final answer.

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

1GHz Smartphone for 1 cent - best deal on a Samsung Galaxy Phone

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