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

[dainceptionman_02]

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?

 

[vanhees71]

I'd say you are right.

 

[kuruman]

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.

 

[TSny]

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?
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.

 

[dainceptionman_02]

Can I take the "region" to be the area enclosed by a plastic loop?
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?

 

[dainceptionman_02]

whoops, i just noticed the question states a region, but not in a conducting loop or geometry.

 

[kuruman]

Can I take the "region" to be the area enclosed by a plastic loop?
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.

 

[TSny]

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.

 

[kuruman]

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.

 

[Charles Link]

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.

 

[TSny]

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.

 

[hutchphd]

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.

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.

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