GR 8677927796770177 | # Login | Register

GR0177 #42
Problem
 GREPhysics.NET Official Solution Alternate Solutions
This problem is still being typed.
Electromagnetism$\Rightarrow$}Faraday Law

Faraday's law suggests that the current inducted opposes the changing field. (This is also known as Lenz Law). It acts something like an electromagnetic inertia.

Since the middle loop is moving towards the observer, the loop A feels an increasing current. Loop A will thus compensate with a current that acts to decrease the field-change; this current is counter-clockwise by the right-hand rule.

Since the middle loop is moving away from loop B, loop B will want to increase its magnetic field, and thus its current is in the same direction as the middle loop.

Only choice (C) works.

(One can immediately cancel out all but choices (A) and (B) from just a conceptual understanding of Lenz Law.)

Alternate Solutions
 secretempire12012-09-04 11:47:18 The best way to think about this problem is the nature does NOT like a change in flux and will attempt to stop it by whatever means necessary. By the right hand rule (curl your fingers in the direction of the current, the magnetic field points in the direction of your thumb), you know that the magnetic field from the current loop flows outward towards A, and inward from B. As the middle loop moves towards A, loop A now sees an excess of incoming flux. And remember, nature does not like changing flux, it will try to maintain what it used to have. So to balance out the new flux, loop A will generate a magnetic field in the opposite direction. By the right hand rule, your thumb is now pointing to the right, and your fingers are curling clockwise, indicating a clockwise current. At the same time, the middle loop is moving away from loop B. Now loop B is seeing a deficiency of flux. Since nature doesn't like to change, loop B will create a magnetic field in the SAME direction to try to boost the flux back up to what it originally was. By the right hand rule, your thumb is pointing to the left, and your fingers are curling counter clockwise, indicating a counter clockwise current.Reply to this comment
secretempire1
2012-09-04 11:47:18
The best way to think about this problem is the nature does NOT like a change in flux and will attempt to stop it by whatever means necessary.

By the right hand rule (curl your fingers in the direction of the current, the magnetic field points in the direction of your thumb), you know that the magnetic field from the current loop flows outward towards A, and inward from B.

As the middle loop moves towards A, loop A now sees an excess of incoming flux. And remember, nature does not like changing flux, it will try to maintain what it used to have. So to balance out the new flux, loop A will generate a magnetic field in the opposite direction. By the right hand rule, your thumb is now pointing to the right, and your fingers are curling clockwise, indicating a clockwise current.

At the same time, the middle loop is moving away from loop B. Now loop B is seeing a deficiency of flux. Since nature doesn't like to change, loop B will create a magnetic field in the SAME direction to try to boost the flux back up to what it originally was. By the right hand rule, your thumb is pointing to the left, and your fingers are curling counter clockwise, indicating a counter clockwise current.
neo55378008
2012-03-23 12:14:43
If a pole approaches a loop, there will be an induced current in such a way that the same pole points back out. If a pole recedes from a loop, the opposite pole will point back out. Then use the right hand rule (thumb along pole, fingers naturally curl in the direction of the current). This can be a little quicker if you're rusty of Lenz's law.

Incoming N produces N
Incoming S produces S
Outgoing N produces S
Outgoing S produces N
memorial
2010-05-31 21:26:29
"the loop A feels an increasing current" ? Do you mean magnetic flux?

istezamer
2009-10-13 00:04:52
I loved the word "Electromagnetic Inertia"!! it really describes what's going on !
 Albert2009-10-28 03:21:31 Yeah, nice term it is, Electromagnetic Inertia. Did you come up with it yourself Yosun? Good! Someone said, strange gestures? Well, we physicists are known for that, aren't we? We do it all our lives :)
 Kabuto Yakushi2010-11-09 13:35:22 Griffiths' "Introduction to Electrodynamics" page 304: "Faraday induction is a kind of 'inertial' phenomenon..." LOL. Oh, and speaking of Griffiths make sure you understand figure 7.22 on the same page..... (hint)
kroner
2009-10-06 14:29:26
Approximately 70 minutes into the test, all of the test takers inexplicably begin staring at their hands while making strange gestures.
ramparts
2009-09-05 07:59:15
A very useful thing to know (this was pointed out by a user in a problem on the 96 test) is that wires with current in the same direction attract, and wires with current in the opposite directions repel. So that with Lenz's law makes this problem a snap - the middle loop will induce a repelling current in A, and an attracting one in B, in an effort to restore the original state.
tat747
2006-10-02 08:37:40
I think there is a typo here. You can cancel out choices (A) and (B), based on a conceptual understanding of Lenz's Law...

Also, the current induced in Loop A will be CLOCK-WISE, thus, choice (C).
 RusFortunat2015-10-16 17:30:41 Yep. I was confused by this typo too.

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}\$ $\frac{a}{b}$