A conceptual question regarding self-inductance

[musicianship]

I have a conceptual question regarding the self-induced emf in a solenoid coil. I have attached a graphic from Serway's Physics for Scientists and Engineers (6th edition) from Chapter 32 (Inductance).

My question is regarding induced emf's (called "Lenz's law emf" in figures (b) and (c)) in the coils; why are they in the shown configuration? It is my understanding that, according to Lenz's Law, the induced emf opposes a change in the magnetic flux of the region surrounded by the coil. By this logic, shouldn't the polarity in (b) be + | - (not - | + as shown) when the current is increasing, thus opposing the change in magnetic flux inside the solenoid and the opposite for (c) where the current is decreasing? Is there a typo, or am I missing something here? Thanks in advanced to anyone who can clarify the polarity of the induced emf for me!

 

[calculus_jy]

i think the book is right as the emf acts like a supplier, in case b opposing the current (see the notion like a battery) so it creates a current going in -------> direction, so -|+ is right and so should case c be right

 

[Defennder]

My question is regarding induced emf's (called "Lenz's law emf" in figures (b) and (c)) in the coils; why are they in the shown configuration? It is my understanding that, according to Lenz's Law, the induced emf opposes a change in the magnetic flux of the region surrounded by the coil. By this logic, shouldn't the polarity in (b) be + | - (not - | + as shown) when the current is increasing, thus opposing the change in magnetic flux inside the solenoid and the opposite for (c) where the current is decreasing? Is there a typo, or am I missing something here? Thanks in advanced to anyone who can clarify the polarity of the induced emf for me!

No, if it were the case for (b) that the induced emf polarity were +|- that would imply that the induced emf is in the same direction as that of the current, when in fact we know that it acts in opposition to the current. The increasing magnetic flux in the diagram which is due to increase in current can be modeled as a bar magnet to the right of the coil with the north pole pointing towards the inductor being pushed to the left. By Lenz law, we would anticipate a induced emf which would generate a magnetic field opposing the bar magnet. In order for it to oppose the N-pole of the magnet, it must itself induce an N at the right of the coil. That corresponds to a an induced emf in -|+.

You can interpret an inductor as a "current resistor" which means to say that for any circuit, the purpose of the inductor would be to keep the current flowing through it at that exact same magnitude and direction.

 

[musicianship]

One thing that I still don't undestand is how does the "Lenz's law emf" interact with the coil? It's my understanding that this is a "battery" that is connected to the corresponding ends of the coil and producing a "counter-current" through the coil. And this current is from + to - as I understand it (assuming this is true, that is why I don't understand why the "Lenz's law emf", when "connected" to the coil, produces a reinforcing current in part (b) which would increase the magnetic flux and a deterring current in part (c) thus further reducing the magnetic flux, instead of the opposite in each case where there would be an opposition to the change in flux). Is this the case? Or is this some kind of emf induced through the cylindrical core? I think my main problem at this point is understand how exactly the Lenz's law emf acts in the coil (how does the current produced by the "Lenz's law emf(s)" in each situation, (b) and (c), travel in the coil, assuming that it does even travel in the coil). Furthermore, how do you infer the effect of the "Lenz's law emf(s)" on the changing magnetic field? Thanks again!

 

[musicianship]

i think the book is right as the emf acts like a supplier, in case b opposing the current (see the notion like a battery) so it creates a current going in -------> direction, so -|+ is right and so should case c be right

So does the induced current run from "- to +" or "+ to -" in the coil? It is my understanding that it is the latter (since I was led to believe that current's direction is that of a positive charge carrier), which is why I'm having trouble understanding...

 

[Doc Al]

One thing that I still don't undestand is how does the "Lenz's law emf" interact with the coil? It's my understanding that this is a "battery" that is connected to the corresponding ends of the coil and producing a "counter-current" through the coil.

There's your problem: You are misinterpreting the diagram's depiction of EMF. Those dashed batteries represent the coil itself, not an external battery connected to the coil. The induced emf is in the coil--the coil is the "battery". And, like any battery, the induced current would flow out of the + terminal and into the - terminal.

So let's look at diagram (b). The current through the coil (which goes from right to left) creates a magnetic field that points left. Since the current is increasing, the magnetic field is increasing. Per Lenz's law the induced EMF and current must oppose that change, thus must point to the right.

In diagram (c), the current is decreasing, so the induced EMF must point to the left.

Make sense?

 

[Defennder]

One thing that I still don't undestand is how does the "Lenz's law emf" interact with the coil? It's my understanding that this is a "battery" that is connected to the corresponding ends of the coil and producing a "counter-current" through the coil. And this current is from + to - as I understand it

You seem to be confusing the voltage polarity for a voltage source (induced emf) and that of a voltage drain (resistor). In a voltage source, current flows from - to +, while in a voltage drain, it flows from + to -. In this case, an induced emf is a voltage source, so this means that -|+ implies that the "counter-current" is in reality flowing from the left-to-right.

(assuming this is true, that is why I don't understand why the "Lenz's law emf", when "connected" to the coil, produces a reinforcing current in part (b) which would increase the magnetic flux and a deterring current in part (c) thus further reducing the magnetic flux, instead of the opposite in each case where there would be an opposition to the change in flux). Is this the case?

There isn't any reinforcing current here. The opposite is true. The current flow is opposed by the coil's inductance. That is accomplished by Lenz law.

Or is this some kind of emf induced through the cylindrical core? I think my main problem at this point is understand how exactly the Lenz's law emf acts in the coil (how does the current produced by the "Lenz's law emf(s)" in each situation, (b) and (c), travel in the coil, assuming that it does even travel in the coil). Furthermore, how do you infer the effect of the "Lenz's law emf(s)" on the changing magnetic field? Thanks again!

To sum it up, the current produced by Lenz law is always in opposition to the original current. That is why the operation of an inductor can be described as that which opposes the change in current, whether the change is increasing or decreasing.