How exactly do inductors work in an LC circuit?

I understand Faraday's law and about induced electric fields created by a changing magnetic fields, etc.

But what causes the current to oscillate in an LC circuit, with no battery? If you picture that there is current going into an inductor, and that current is decreasing over time, then you would see a curly electric field being produced in the direction of the current flow. (I uploaded an image for my reasoning)

Also, why would the current decrease at all? If inductors "oppose" change, wouldn't it make sense that the curly electric pushes the current to counteract the decreasing Coulombic electric fields?

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The decreasing current in the inductor does indeed produce a change in the magnetic field that makes the current continue.
The current however is going into the capacitor and the voltage across the capacitor will increase, and that will make the current stop and then change sign.

Dale
Mentor
2021 Award
But what causes the current to oscillate in an LC circuit, with no battery?
##v= L\frac{d}{dt}i## and ##i=-C\frac{d}{dt}v##
so ##i=-LC\frac{d^2}{dt^2}i##
and therefore the current oscillates

DaveE
tech99
Gold Member
I understand Faraday's law and about induced electric fields created by a changing magnetic fields, etc.

But what causes the current to oscillate in an LC circuit, with no battery? If you picture that there is current going into an inductor, and that current is decreasing over time, then you would see a curly electric field being produced in the direction of the current flow. (I uploaded an image for my reasoning)

Also, why would the current decrease at all? If inductors "oppose" change, wouldn't it make sense that the curly electric pushes the current to counteract the decreasing Coulombic electric fields?
An inductor is rather similar to a mass in mechanics; it has an inertia action. If we try to stop a moving mass, it opposes us with a force which equals the braking force we are applying (Newton). So there is an equilibrium, but it only exists when deceleration is taking place.

sophiecentaur
The decreasing current in the inductor does indeed produce a change in the magnetic field that makes the current continue.
The current however is going into the capacitor and the voltage across the capacitor will increase, and that will make the current stop and then change sign.
Why would the capacitor the capacitor gain voltage if it was initially charged with no battery?

What I was trying to get at was what drives the current in the opposite direction? There has to be some electric or magnetic field that causes it to reverse. Near the end of one period, the current and the capacitor potential is nearly zero. If it was the electric field of the inductor , wouldn't the field have to be in the same plane as the circuit in order to drive current?

anorlunda
Staff Emeritus
Why would the capacitor the capacitor gain voltage if it was initially charged with no battery?
Because the current from the inductor also goes through the capacitor. Current in a capacitor makes its voltage change.

Did you understand @Dale 's answer in #3?

Because the current from the inductor also goes through the capacitor. Current in a capacitor makes its voltage change.
During a period, there is current going into the capacitor but that doesn't mean an increase in potential because it matters what the net charge over the capacitor plates are. So that doesn't make sense to me.

Did you understand @Dale 's answer in #3?
Yes I mean I understand but I don't know where it came from. What I want to know is what microscopic aspect of it causes the current to want to suddenly change directions.

anorlunda
Staff Emeritus
During a period, there is current going into the capacitor but that doesn't mean an increase in potential because it matters what the net charge over the capacitor plates are. So that doesn't make sense to me.
That remark doesn't make sense to me. Current through a capacitor changes the charge on the capacitor plates. "Net charge" is always zero, one plate has an excess of plus the other plate has an excess of minus. When we say that the capacitor is charged, we mean that there is a differential between the plates.

What do you think charged capacitor means?

That remark doesn't make sense to me. Current through a capacitor changes the charge on the capacitor plates. "Net charge" is always zero, one plate has an excess of plus the other plate has an excess of minus. When we say that the capacitor is charged, we mean that there is a differential between the plates.

What do you think charged capacitor means?
I mean of how a capacitor is initially fully charged, and over time the electric field of the capacitor weakens because the charge buildups cancel each other out. So then over time the potential and the current goes to zero.

anorlunda
Staff Emeritus
I mean of how a capacitor is initially fully charged, and over time the electric field of the capacitor weakens because the charge buildups cancel each other out. So then over time the potential and the current goes to zero.

That sounds completely wrong, but maybe you are thinking of a different scenario than I am. With DC, the current goes to zero, but the voltage stays the same.
##I=C\frac{dV}{dt}##

Perhaps you are thinking about leakage in an imperfect capacitor.

Can you draw a circuit that demonstrates what you're talking about? Use a battery, resistor, and a capacitor. Take a picture of it with good lighting, then use the UPLOAD button to post it.

Can you draw a circuit that demonstrates what you're talking about? Use a battery, resistor, and a capacitor. Take a picture of it with good lighting, then use the UPLOAD button to post it.
What I'm thinking about is a capacitor and a resistor for example. With no battery. Initially at ##t=0## the capacitor is fully charged and has some potential across it's plates. Over time, the current falls of as ##I=\frac{emf}{R}e^{\frac{-t}{RC}}## therefore the potential of the capacitor drops as well. We can see an example here: http://www.falstad.com/circuit/e-cap.html (just imagine that there is no battery and the capacitor has an initial potential ##\Delta V##

Coming back to my original question. In this RC circuit, now if we place an inductor in it, this happens.

My question is why does this happen? What force/field makes the current go the other way?

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Dale
Mentor
2021 Award
I don't know where it came from
The definition of a capacitor is ##i= C \frac{d}{dt} v##. In other words, a capacitor is a device where the current through the device is proportional to the change in the voltage across it.

The definition of an inductor is ##v=L\frac{d}{dt} i##. In other words an inductor is device where the voltage across the device is proportional to the change in the current through it.

In a LC circuit the current through each device is the same and the voltage across them is opposite, so when you write the expression for the circuit you get ##i = -LC \frac{d^2}{dt^2} i ##, which we immediately recognize as the equation of an oscillator.

What I want to know is what microscopic aspect of it causes the current to want to suddenly change directions.
All of the changes are gradual. There are no sudden changes.

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The definition of a capacitor is ##i= C \frac{d}{dt} v##. In other words, a capacitor is a device where the current through the device is proportional to the change in the voltage across it.

The definition of an inductor is ##v=L\frac{d}{dt} i##. In other words an inductor is device where the voltage across the device is proportional to the change in the current through it.

In a LC circuit the current through each device is the same and the voltage across them is opposite, so when you write the expression for the circuit you get ##i = -LC \frac{d^2}{dt^2} i ##, which we immediately recognize as the equation of an oscillator.

All of the changes are gradual. There are no sudden changes.
What field causes the current to change direction?

sophiecentaur
Gold Member
What field causes the current to change direction?
The Charge on the Capacitor builds up so eventually the volts increase and become greater than the emf induced in the inductor and the current reverses. The process repeats in the other direction etc. etc.
You also say "During a period, there is current going into the capacitor but that doesn't mean an increase in potential" and that is wrong. Current flowing into a capacitor will change the PD.

Dale
Mentor
2021 Award
What field causes the current to change direction?
Both the capacitor and the inductor are necessary. It is like asking if the spring or the mass causes the velocity to reverse in a mass-spring oscillator. Without both parts you don’t get oscillation.

That said, at the moment when the current switches from positive to negative (or vice versa) the magnetic field is zero and the electric field is maximum.

Asymptotic, Zack K and sophiecentaur
Mister T
Gold Member
Also, why would the current decrease at all?
Something unmentioned is causing the current to decrease. Perhaps a hand is turning a knob, or a battery is discharging.

Mister T
Gold Member
I understand Faraday's law and about induced electric fields created by a changing magnetic fields, etc.

But what causes the current to oscillate in an LC circuit, with no battery?

Changing electric fields also induce magnetic fields.

You also say "During a period, there is current going into the capacitor but that doesn't mean an increase in potential" and that is wrong. Current flowing into a capacitor will change the PD.
So why does the voltage of an RC circuit with no battery drop to zero over time?
The Charge on the Capacitor builds up so eventually the volts increase and become greater than the emf induced in the inductor and the current reverses
I'm talking about an LC circuit with no battery. To my understanding, a fully charged capacitor discharges and over time the fringing fields of the capacitor decrease because the original charge imbalance on the capacitor balances over time as electrons move from the negative plate, to the positive one until they cancel each other out. But the inductor reverses that?

Something unmentioned is causing the current to decrease. Perhaps a hand is turning a knob, or a battery is discharging.
I know that's not possible obviously, but you took that out of context. Wouldn't it be reasonable to say that this inductor creates an electric field to oppose the decrease in current, and in doing so the electric field never decreases. (I uploaded an image of my reasoning).

Both the capacitor and the inductor are necessary. It is like asking if the spring or the mass causes the velocity to reverse in a mass-spring oscillator. Without both parts you don’t get oscillation.

That said, at the moment when the current switches from positive to negative (or vice versa) the magnetic field is zero and the electric field is maximum.
And you can fundamentally explain that can't you? So the springs are made of some material who's molecules like to be positioned the way they are, and when displaced will exert a force the opposite way to go back to their original position, probably due to how they bind geometrically (I'm not sure). So what fundamental aspect of an inductor makes it want to reverse current?

Dale
Mentor
2021 Award
And you can fundamentally explain that can't you?
I already did! Starting from the definition of a capacitor and an inductor and deriving it explicitly for you step by step. What part of the derivation did you not follow? You have not asked a single specific question about it.

Any time you get a function of the form ##\frac{d^2}{dt^2}x = -k x## you have an oscillator. Do you understand that? And if so did you understand my derivation?

So what fundamental aspect of an inductor makes it want to reverse current?
It is not just the inductor, it is the combination of both the inductor and the capacitor, as I showed above.

I already did! Starting from the definition of a capacitor and an inductor and deriving it explicitly for you step by step. What part of the derivation did you not follow? You have not asked a single specific question about it.
I understand your derivation and I can see that it shows oscillation. I'm more wanting to know what's going on microscopically.

##\frac{d^2}{dt^2}x=-kx##. But why? Why does this oscillation occur? Why is there a restoring force? (those are rhetorical questions) All that can be explained to an extent on a somewhat fundamental level. Maybe you have already explained it but I haven't picked up on it.

You can say it in the most layman terms possible.

So an RC circuit eventually loses all it's current. An inductor now in that circuit opposes the change and tries to increase the current (to my understanding). But how exactly does it oppose this change?

Dale
Mentor
2021 Award
I'm more wanting to know what's going on microscopically.
I have no idea what you mean by this. The size of the capacitor and inductor is not relevant.

You can say it in the most layman terms possible
Then why did you mark the thread as intermediate? If you want basic answers you should mark your thread as basic. This is highly frustrating

So an RC circuit eventually loses all it's current. An inductor now in that circuit opposes the change and tries to increase the current (to my understanding). But how exactly does it oppose this change?
Current is not a conserved quantity so it makes little sense to say that a circuit loses its current. What it loses is its energy. The energy is dissipated in the resistor as heat. For the inductor the energy is not dissipated but is temporarily stored in the inductor in its magnetic field. So the difference is that a RC circuit loses energy and a LC circuit does not.

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Zack K
So an RC circuit eventually loses all it's current. An inductor now in that circuit opposes the change and tries to increase the current (to my understanding). But how exactly does it oppose this change?

It's the capacitors task to make the current change.

Inductor :

1: drains the capacitor smoothly - not short circuiting
2: charges the capacitor to reverse polarity
3: drains the capacitor smoothly - current is now opposite to 1

Zack K
I have no idea what you mean by this. The size of the capacitor and inductor is not relevant.

Then why did you mark the thread as intermediate? If you want basic answers you should mark your thread as basic. This is highly frustrating

Current is not a conserved quantity so it makes little sense to say that a circuit loses its current. What it loses is its energy. The energy is dissipated in the resistor as heat. For the inductor the energy is not dissipated but is temporarily stored in the inductor in its magnetic field. So the difference is that a RC circuit loses energy and a LC circuit does not.
Sorry, I didn't mean to frustrate you.

I think I understand, but the answer wasn't to what I expected to be about so I was confused.