GREPhysics.NET: GR9677 #89

GR9677 #89

Problem

GREPhysics.NET Official Solution

This problem is still being typed.

Electromagnetism $\Rightarrow$ }Trajectory

The only physics involved in this problem is equating the centripetal force with the Lorentz Force, $mv^2/R=qvB$ . The rest is math manipulation and throwing out terms of ignorable order.

The radius of curvature used in the centripetal force equation is given by $R^2=l^2+(R-s)^2$ , and ETS is nice enough to make this geometry fairly obvious in the diagram enclosed with the original question.

Now, note that since $s<<l$ , after expanding the expression for $r^2$ , one can drop out terms of higher order. Thus, $R^2=l^2+(R-s)^2=l^2+R^2+s^2-2Rs\approx l^2+R^2-2Rs + O(s^2)$ . Canceling the R's on both side, one finds, $l^2=2Rs \Rightarrow R = l^2/(2s)$ . Plug this into the force equation above to find,

$mv/R = qB \Rightarrow 2smv/l^2=qB \Rightarrow p=mv=qbl^2/2s, <br />$

which is choice (D).

Alternate Solutions

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

Comments

askewchan 2008-11-06 19:41:29	Also, we can eliminate (A) and (B) because we know that a larger $s$ implies greater acceleration which means lower momentum. The same goes for a smaller $l$ . In other words, if the particle has great momentum the radius of this arc will be larger, which gives a greater $l$ and lesser $s$ . Reply to this comment
cordercom 2008-10-05 18:23:40	At the very least we can eliminate choice (C) by units. 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...

Chat Archives | Delete left banner ad | Donate

(Click to view chat.)

Hate being Anonymous? Login or Register

Upgrade to Poser 7 Now

Huge Textbook Selection, Low Prices – Phat Campus.

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