Lenz's law

[brood910]

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33.6 There is a ccw-induced current in the conducting loop shown in the figure. Is the magnetic field inside the loop increasing in strength, decreasing in strength, or steady?


I know that the induced magnetic field is out of the page. That means, the current was induced to oppose the increase in the original magnetic field that is going into the page.

So, the current will decrease the magnetic field in the loop.

Is my reasoning correct here?



Also, in TBR, it says "current is induced only when the loop is entering or leaving the magnetic field". How is this true when current is also induced when there's a change in the strength of B + when voltage is applied?

 

[Mission Medical]

33.6 There is a ccw-induced current in the conducting loop shown in the figure. Is the magnetic field inside the loop increasing in strength, decreasing in strength, or steady?


I know that the induced magnetic field is out of the page. That means, the current was induced to oppose the increase in the original magnetic field that is going into the page.

So, the current will decrease the magnetic field in the loop.

Is my reasoning correct here?



Also, in TBR, it says "current is induced only when the loop is entering or leaving the magnetic field". How is this true when current is also induced when there's a change in the strength of B + when voltage is applied?

Yes, that's basically the idea. One way to think about it is that, using the right hand rule, a magnetic field out of the page should be producing a counterclockwise current. When we're talking about induced currents, a magnetic field out of the page is the same as a magnetic field into the page that's decreasing.

With regards to TBR, the point that the book is trying to make is that current is only induced in a loop if the flux of magnetic field through the loop changes, and that can only occur when the loop leaves or enters the magnetic field. Why is this? When the loop enters the field, we are going from a starting condition of no magnetic flux into the loop to a condition where magnetic flux starts entering the loop, so there is an increase in flux. When the loop leaves the magnetic field, we are going from flux going through the loop to no flux through the loop, so now there's a decrease in flux.

If the loop isn't leaving or entering, then the entire loop is submerged in a constant magnetic field, so there's no change in magnetic flux through the loop. By the way, we are assuming this whole time that the magnetic field we are talking about is constant. If it's changing, then that complicates the situation.

 

[sakabato93]

33.6 There is a ccw-induced current in the conducting loop shown in the figure. Is the magnetic field inside the loop increasing in strength, decreasing in strength, or steady?


I know that the induced magnetic field is out of the page. That means, the current was induced to oppose the increase in the original magnetic field that is going into the page.

So, the current will decrease the magnetic field in the loop.

Is my reasoning correct here?



Also, in TBR, it says "current is induced only when the loop is entering or leaving the magnetic field". How is this true when current is also induced when there's a change in the strength of B + when voltage is applied?

The induced current in the wire is due to the fact that a changing magnetic flux will induce a voltage. The induced current from the voltage will flow such that the magnetic flux formed by the induced current will oppose the initial change in magnetic flux. The flux from the induced current in your picture will flow inward, which, but the right hand rule, implies that the induced current flows clockwise which opposes the initial clockwise flow, decreasing it.

 

[Mission Medical]

I sort of forgot to answer the last part of your question. So basically, what TBR said is indeed true, but that's specifically when we're talking about a magnetic field that's constant. You're also right. If that loop is submerged in a constant magnetic field with constant magnetic flux through the loop, but then all of a sudden the field strength increases, then more flux starts going through the loop, so a current is induced. In this scenario we don't require the loop to enter or leave the magnetic field for the flux to change. The flux is changing now because we are increasing the magnetic field strength.

 

[brood910]

Sweet.
Im happy that I finally got this down.

Thanks everyone for the confirmation.