GREPhysics.NET
GR | # Login | Register
   
  GR9677 #69
Problem
GREPhysics.NET Official Solution    Alternate Solutions
This problem is still being typed.
Electromagnetism}Ampere Law

Recall Ampere's Law, \vec{B} \cdot d\vec{l} = \mu_0 I_{i<i>n</i>.

Since the region one is interested in is a vacuum, one's Ampere Loop encloses all of the current. Thus, the field from each conductor is B(2\pi r) = \mu_0 J \pi R^2, where, I_{i<i>n</i> = J \pi R^2 and R is the radius of the conductor. (This is a good approximation of the current, as one assumes that the vacuum region in the center is small compared to the area of the conductors.)

Making the approximation that R\approx d/2, one has B = \frac{\mu_0 J \pi R^2}{2\pi R}\approx \frac{\mu_0 J \pi d}{4\pi}. Since both fields contribute in the center, the field is twice that, \frac{\mu_0 J \pi d}{2\pi}, as in choice (A).

(Also, one can immediately eliminate all but choices (A) and (B) by the right-hand rule. One seeks a +y-direction field.)

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
Richard
2007-10-01 18:35:55
One should note that by geometry there will be no dependence on the radius r in the solution:
Thus (a) is the answer.
Alternate Solution - Unverified
sharpstones
2006-11-30 12:23:41
It would be easier to not consider any vacuum in the center. Since you have current flowing in opposite directions they will naturally cancel each other out in the middle. Simple find the field at A due to one of the cylinders of current(it will be a distance d/2 from the center) and then multiply times 2. Alternate Solution - Unverified
Comments
bucky0
2007-10-02 19:22:28
Don't the fields cancel? If the currents are equal traveling in each direction, you should end up with the same B field contribution from each side, but in opposite directions, which would drop it to zero, correct?
antithesis
2007-10-04 20:48:53
But one is on the right of A, and one is to the left, so that they add up (think of right hand rule)
NEC
Richard
2007-10-01 18:35:55
One should note that by geometry there will be no dependence on the radius r in the solution:
Thus (a) is the answer.
ewhite2
2007-10-30 18:57:02
why?
FortranMan
2008-08-29 12:47:04
because increasing the radius, while increasing the distance between their centers, would also increase the current, hence the answer should not be proportional to the inverse of r. Only d really matters in the magnitude of the field.
hanin
2009-09-29 22:37:52
Why increasing radius would also increase current? I imagine this like 2 pipes carrying water; no matter how much you enlarge your your pipe, the same amount of water will always flow if there is no change in the source.
dogsandfrogs
2009-10-08 12:24:51
Current is given as a current density, not a set value. Density is the same regardless of r, hence why the answer should not depend on r.
Alternate Solution - Unverified
sharpstones
2006-11-30 12:23:41
It would be easier to not consider any vacuum in the center. Since you have current flowing in opposite directions they will naturally cancel each other out in the middle. Simple find the field at A due to one of the cylinders of current(it will be a distance d/2 from the center) and then multiply times 2. Alternate Solution - Unverified
santon
2006-11-02 15:08:53
NEC
yosun
2005-11-11 21:24:16
keflavich: thanks for the typo-alert; it has been corrected. NEC
keflavich
2005-11-11 18:27:43
Typo: "All but choices A and B because they have a +y field" should probably replace the last thing in parentheses. NEC

Post A Comment!
Username:
Password:
Click here to register.
This comment is best classified as a: (mouseover)
 
Mouseover the respective type above for an explanation of each type.

Bare Basic LaTeX Rosetta Stone

LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces .
type this... to get...
$\int_0^\infty$
$\partial$
$\Rightarrow$
$\ddot{x},\dot{x}$
$\sqrt{z}$
$\langle my \rangle$
$\left( abacadabra \right)_{me}$
$\vec{E}$
$\frac{a}{b}$
 
The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...


ShoutMix chat widget

College is Hard - Research is Easy

Find Scholarships Today!

$3.4 Billion in Scholarships

SL Button 125

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.

90% Off + FREE SHIPPING!

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