Induced EMF in Rectangular Loop in B-Field

Click For Summary

Discussion Overview

The discussion revolves around the concept of induced electromotive force (emf) in a rectangular loop moving within a uniform magnetic field. Participants explore the implications of the loop's motion, the forces acting on charges within the loop, and the conditions under which emf is generated or canceled out.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether moving a rectangular loop in a uniform magnetic field induces an emf, suggesting that there should be a current due to the forces acting on the loop.
  • Another participant clarifies that the answer referred specifically to the induced emf, not the current.
  • It is noted that while the top and bottom sides of the loop are parallel to the motion and thus do not contribute to induced current, the left and right sides may experience opposing currents.
  • A participant explains that while the Lorentz force acts on the conduction electrons, the uniform magnetic field leads to a net emf of zero due to cancellation between opposing segments of the loop.
  • One participant proposes an analogy of attaching two batteries in parallel to illustrate the potential difference across the loop, questioning if this leads to a net emf of zero according to Kirchhoff's loop rule.
  • Another participant agrees with the Kirchhoff's loop simplification, stating that while there is an emf, it is canceled out when summing the contributions from opposite sides of the loop.
  • Discussion includes the idea that if the top and bottom of the loop are considered as thin rods, they would not experience induced emf due to the Lorentz force.
  • Faraday's Law is referenced to support the argument that if the magnetic field and loop are constant, there is no net flux change, leading to zero emf.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which induced emf occurs, with some arguing that the emf is canceled out while others explore the implications of forces acting on charges. The discussion remains unresolved regarding the interpretation of emf in this context.

Contextual Notes

Participants acknowledge the complexity of the situation, including the dependence on the uniformity of the magnetic field and the geometry of the loop. The discussion highlights the nuances in applying concepts like Lorentz force and Faraday's Law to the scenario presented.

quietrain
Messages
648
Reaction score
2
ok, if i have a rectangular loop parallel to the screen and in a uniform constant magnetic field pointing perpendicularly outwards of the screen, if i move the loop to the right of the screen, will there be an induced emf in the loop?

my understanding is that there will be? because we have a force to the right , b-field outwards of the screen, and by fleming's left hand rule we get a current heading upwards of the screen?

but why is the answer no emf? is it because of mutual cancellations within the loop or something? or is my concept totally wrong?

thanks
 
Physics news on Phys.org
Was the answer referring to the emf or to the current?
 
the answer was referring to the induced emf.

also i realize, the current would be heading upwards on the left side of the loop, and also heading upwards on the right side of the loop. so wouldn't the current be warring each other?
also, the top and bottom sides are parallel to the motion so i assume no induced current in them?
 
By pulling the loop, you are giving the charges in the loop a velocity. By the Lorentz law then, there is a force acting on the conduction electrons in the wire. So the top and bottom parts of the loop will also experience a force and hence an EMF.

However, because the magnetic field through the loop is uniform, the net EMF is zero. This is due to the phenomenon that you already surmised. That is, the EMF induced on the right hand wire is canceled out by the EMF induced on the left hand wire. Like wise for the top and bottom. So while a straight section of wire does experience an EMF, it is canceled out by the section's mirror image on the other side of the current loop.

Now if the magnetic field differs on opposite sides, that is the magnetic field is nonuniform, then we can experience a net EMF since the net force on opposite segments is no longer zero.
 
so let's say the positive charges get pushed downwards by the induced force, so it would be like attaching 2 batteries in parallel?
- _-
| |
| |
| |
+_+

so postiive potential at the bottom, negative on top..

so the emf othe right side is let's say 5V. then the emf of the left side is also 5 votes.

so by kirchhoffs loop rule, it will be 5+-5 = 0? so net emf = 0?

btw, if we assume the top and bottom to be thin rods, then the charges would not be moved by the lorentz force right? so no induced emf in those portions?
 
quietrain said:
so let's say the positive charges get pushed downwards by the induced force, so it would be like attaching 2 batteries in parallel?
- _-
| |
| |
| |
+_+

so postiive potential at the bottom, negative on top..

so the emf othe right side is let's say 5V. then the emf of the left side is also 5 votes.

so by kirchhoffs loop rule, it will be 5+-5 = 0? so net emf = 0?

btw, if we assume the top and bottom to be thin rods, then the charges would not be moved by the lorentz force right? so no induced emf in those portions?

As to your Kirchoff loop simplification, that is correct. There still exists an EMF, but the EMF from opposite sections of wire oppose each other when we sum it all up. This would be true for a closed loop of arbitrary shape but it is easier to show it with a rectangular loop.

Yes, if we assume a rod of zero radius then the electrons would not move, but there would still be a force acting on the charges. What technically happens here is that the Lorentz force induces the negative electrons to try and separate from the positive ionic lattice of the wire. As they separate spatially, there arises a restorative Coulombic force between the electrons and the ions. So with a one-dimensional wire, the EMF is countered by the Coulombic attraction that keeps the charges from moving in a direction other than along the wire. So it exists for a fleeting moment as it does a momentary amount of work but gets canceled out in steady-state. Whether or not you consider it to be an EMF is probably just a technical point, probably not considering that EMF usually refers to the net effect.
 
The explanations in terms of the Lorentz force are correct, of course. It is also possible to think in terms of Faraday's Law to help understand this one.

Consider the most general form of Faraday's Law in integral form as follows.

[tex] EMF=\ointop_{\partial S} E \cdot dl=-{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)<br /> [/tex]

Here it is clear that if the magnetic field is constant, and if the loop is constant, there is no net flux change as the loop is moved. Hence, the EMF must be zero.
 
ah i see. thanks!
 

Similar threads

Undergrad Questions about cancelation of induced EMF and minimizing eddy currents
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Electric Fields with Motional EMF
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Faraday induction in constant B field, with non-conduction wires
  • · Replies 2 ·
Replies
2
Views
2K
High School EMF Induction in a Loop of Wire - Does It Work?
  • · Replies 3 ·
Replies
3
Views
18K
High School How do you calculate induced EMF in an open loop with changing magnetic field?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Expanding loop torque division
  • · Replies 3 ·
Replies
3
Views
438
Undergrad Motional EMF in Faraday disc, co-rotating magnet axial mean flux
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Derivation of induced voltage in loop
  • · Replies 32 ·
2
Replies
32
Views
3K
Undergrad B-Fields: Deriving Faraday's Law & Why No Work?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Why is there an induced EMF in this case?
  • · Replies 12 ·
Replies
12
Views
3K