A (nonconservative) electric field is induced in any region in which...

In summary: I'm not sure what scenario you have in mind. I was trying to come up with a scenario where...In summary, the answer to the question is B.
  • #1
dainceptionman_02
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Thread moved from the technical forums to the schoolwork forums
TL;DR Summary: A (nonconservative electric field is induced in any region in which)
A. there is a changing magnetic flux
B. there is a changing magnetic field
C. the inductive time constant is large
D. the electrical resistance is small
E. there is electrical current

there can be more than one answer

I put A and B, but the answer was B, only when there is a changing magnetic field. i re-read the section and it only mentions a changing magnetic field, but not a change in flux, however, the equation states ∫E⋅ds=-dΦ/dt, which is the change in flux, so can't it be both?
 
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  • #2
I'd say you are right.
 
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  • #3
If the answer is supposed to be only (B), then I would say that this is not a well-designed question. The answer could also be (E), "there is electrical current." The current generates a magnetic field and if the current is changing (we are not told that it isn't), then there would be a changing magnetic field and hence a non-conservative electric field in the region.
 
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  • #4
dainceptionman_02 said:
TL;DR Summary: A (nonconservative electric field is induced in any region in which)
A. there is a changing magnetic flux
Can I take the "region" to be the area enclosed by a plastic loop? :oldsmile:
Rotate the loop in a time-independent magnetic field. The changing magnetic flux through this "region" does not induce a nonconservative electric field.

I agree that there are semantic ambiguities with the wording of the question.
 
  • #5
TSny said:
Can I take the "region" to be the area enclosed by a plastic loop? :oldsmile:
Rotate the loop in a time-independent magnetic field. The changing magnetic flux through this "region" does not induce a nonconservative electric field.

I agree that there are semantic ambiguities with the wording of the question.
but changing the area or rotating the loop does induce a voltage therefore it should induce an electric field? there is the statement that a changing magnetic field induces an electric field, but couldn't an electric field also be induced by changing the area or angle, aka magnetic flux?
 
  • #6
whoops, i just noticed the question states a region, but not in a conducting loop or geometry.
 
  • #7
TSny said:
Can I take the "region" to be the area enclosed by a plastic loop? :oldsmile:
Rotate the loop in a time-independent magnetic field. The changing magnetic flux through this "region" does not induce a nonconservative electric field.
I don't think that this works as a counterexample. The existence of a non-conservative electric field should not depend on whether there are charges free to move in the loop that is rotating.
 
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  • #8
kuruman said:
I don't think that this works as a counterexample. The existence of a non-conservative electric field should not depend on whether there are charges free to move in the loop that is rotating.
The reason I chose a plastic loop was to avoid having any induced current in the rotating loop. If the loop were a conductor, then the current induced in the loop would generate its own B field and this field would be changing with time. This time-dependent B field would induce a nonconservative E field.

I was thinking that if the loop is plastic, then we would not get an induced current. So there wouldn't be an induced, nonconservative E field in this case.

But there would be a time-dependent induced emf in the plastic loop: $$ \rm {emf} =\oint_{\rm loop} \left( \mathbf{v} \times \mathbf{B} \right) \cdot \mathbf{dl} $$ where ##\mathbf{v}## is the velocity of the loop element ##\mathbf{dl}## and ##\mathbf{B}## is the uniform, time-independent field in which the loop is rotating. So, the induced emf would not involve a nonconservative E field.

I was trying to find a justification for not allowing choice A to be a correct answer.
 
  • #9
TSny said:
I was trying to find a justification for not allowing choice A to be a correct answer.
I think that this is a poorly formulated question and that we should leave it at that. Within the formulation as presented, I can think of a justification for not allowing choice (B) to be the correct answer. If the region of space contains a static magnetic field that is non-uniform, then the field is "changing" in that region, yet there is no induced non-conservative electric field.
 
  • #10
Might I comment on this: I think the induced EMF, i.e. the E field from it, is in general non-conservative, because ## \nabla \times E=-\dot{B} ## is non-zero. Thereby ## \oint E \cdot dl =-\dot{\Phi} ## is non-zero.
 
  • #11
Charles Link said:
Might I comment on this: I think the induced EMF, i.e. the E field from it, is in general non-conservative, because ## \nabla \times E=-\dot{B} ## is non-zero. Thereby ## \oint E \cdot dl =-\dot{\Phi} ## is non-zero.
I'm not sure what scenario you have in mind. I was trying to come up with a scenario where ##\dot{\Phi} \neq 0##, but ##\large \frac{ \partial \mathbf{B}}{\partial t} = 0##. So, in this case, ##\nabla \times \mathbf{E} = 0## and ##\mathbf{E}## would be conservative.

The formula ## \oint E \cdot dl =-\dot{\Phi} ## does not generally hold in "motional emf" scenarios, such as the rotating loop example.

The relation ## \nabla \times \mathbf{E}=-\frac{ \partial \mathbf{B}}{\partial t} ## implies ##\oint \mathbf{E} \cdot \mathbf{dl} =-\int \frac{\partial \mathbf{B}}{\partial t} \cdot \mathbf{dA}. \,\,## But ##\int \frac{\partial \mathbf{B}}{\partial t} \cdot \mathbf{dA}## does not always reduce to ##\dot{\Phi} ##.

Move a loop of fixed shape and orientation through a nonuniform, time-independent B field such that the movement causes ##\Phi## through the loop to change with time. Here, ## \oint E \cdot dl =0## since ##\large \frac{ \partial \mathbf{B}}{\partial t} = 0##. So, we can have a changing magnetic flux through the loop without the existence of a nonconservative E field. The rotating loop in a uniform, time-independent B field is a similar example.
 
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  • #12
Charles Link said:
I think the induced EMF, i.e. the E field from it
This is very bad terminology IMHO, for reasons we have talked about before.


kuruman said:
If the answer is supposed to be only (B), then I would say that this is not a well-designed question. The answer could also be (E), "there is electrical current." The current generates a magnetic field and if the current is changing (we are not told that it isn't), then there would be a changing magnetic field and hence a non-conservative electric field in the region.
I don'tthink so If you look at the inference in the question (E) is not an answer.
dainceptionman_02 said:
A (nonconservative electric field is induced in any region in which)
There is not an induced E field in every region where there is a current. (E) is incorrect.
I believe the answer (A) is incorrect because there can be changing flux through a region whose shape is changing
Not my favorite question however
 

FAQ: A (nonconservative) electric field is induced in any region in which...

What does it mean for an electric field to be nonconservative?

A nonconservative electric field is one in which the work done by the field on a charged particle depends on the path taken by the particle. This is in contrast to a conservative electric field, where the work done is independent of the path and depends only on the initial and final positions.

How is a nonconservative electric field induced?

A nonconservative electric field is induced in any region where there is a time-varying magnetic field. According to Faraday's Law of Induction, a changing magnetic field creates a circulating electric field, which is nonconservative in nature.

What is Faraday's Law of Induction?

Faraday's Law of Induction states that a time-varying magnetic field induces an electromotive force (EMF) and consequently an electric field in a closed circuit. Mathematically, it is expressed as EMF = -dΦB/dt, where ΦB is the magnetic flux through the circuit.

Can a nonconservative electric field exist in a static magnetic field?

No, a nonconservative electric field cannot exist in a static magnetic field. A static magnetic field does not change with time, and therefore, according to Faraday's Law, it cannot induce an electric field. A nonconservative electric field requires a time-varying magnetic field.

What are some practical applications of nonconservative electric fields?

Nonconservative electric fields are fundamental to the operation of many electrical devices and technologies, such as transformers, electric generators, and induction motors. These devices rely on the principles of electromagnetic induction to convert mechanical energy to electrical energy and vice versa.

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