 Let's solve a couple of questions on factors that affect mutual inductance. For the first one, we have two coils that are placed in two different orientations with respect to each other. And we can see these two orientations. In which case is the mutual inductance between the coils greater? The distance between the centers, we can see that is D that remains unchanged. Choose one answer out of these three options. Alright, as always, why don't you try this question on your own first. Alright, hopefully you have given this a shot. Now, let's try to recall what was mutual inductance to begin with. So, for mutual inductance, let's say, if we have a current running in this coil, let's choose this brush. If we have a current running in this coil like this. Now, because of the current in this coil, there will be, there will be, as a result of that, there will be some magnetic field lines produced. And if you try to draw them, if you try to draw them, so let's, let's do that. And the magnetic field lines can look somewhat, somewhat like this. So, they go in and they come out from here and there will be more magnetic field lines which look, which look like this. Okay. Alright, good enough. Now, these magnetic field lines, they might be passing through the other coil. And as a result of that, the magnetic flux through the other coil changes. And we know from Faraday's law, whenever there is a changing magnetic flux, there will be an EMF induced. But that EMF will be in opposition to the change in flux. It will try to oppose the change in flux. And that is what Lenz's law says. So, as a result of the current flowing in one coil, we have an EMF induced in the other coil which try to oppose this, the change in flux, the change in the number of magnetic field lines passing through it. That really gives rise to mutual inductance. Now, in this case, if we have a current flowing in anti-clockwise direction in coil one, and similar type of current flowing in coil two. So, we will have magnetic field lines which will, which will, which will look like this. In the first orientation, not many magnetic field lines will pass through the coil. And as a result of that, the flux, the magnetic flux through coil, the blue coil won't really change much. So, even the opposition, the oppositional EMF, even that would be extremely less. Just a slight number of magnetic field lines are passing through it. But look at the second orientation. The number of magnetic field lines passing through the blue coil is much greater, is much greater. So, as a result of which the magnetic flux changes by a higher amount. And that results in higher oppositional EMF and higher mutual inductance. So, we can say that in this one, the right answer is case two. Okay. Let's look at one more question. All right. So, for this one, we have a pair of solenoids, which are having a mutual inductance M. And we can see the pair of solenoids like this. Current of a certain magnitude is flowing through the inner solenoid. What is the effect of increasing the magnitude of current flowing in the inner solenoid? All right. Now, for this one, we have a pair of solenoids. And we can think about the mutual inductance. So, we can say either the mutual inductance of the outer solenoid with respect to the inner one, or we can write, we can write mutual inductance of the inner solenoid with respect to the outer one. The good thing is that these two are equal. These two are equal to each other. Okay. Now, when there is a current flowing in the inner solenoid, there will be magnetic field lines produced due to that. There will be some magnetic flux. And as a result of magnetic flux passing through the coils of the outer solenoid, there will be an EMF. And the EMF will oppose that change in flux, right? Rim Lenses Law. So, okay. Let's write that. Let's write that EMF. Let's write that EMF. So, EMF in the outer solenoid, this is equal to, this is equal to the mutual inductance of the outer solenoid with respect to the inner one into the rate of change of current in the inner solenoid, right? Because there is a current in the inner solenoid because of which there is an EMF in the outer solenoid, right? So, rate of change of current in the inner solenoid. Okay. Now, the question says that the current of a certain magnitude is flowing, all right? What is the effect of increasing that magnitude of current? So, this current I inner that is being increased. What does that do to the mutual inductance? Well, to figure that out, what I like to do is I like to, I like to take this constant of MOI, I like to take this inside. And why do I do that? That is because I know from Faraday's law, whenever there is an EMF induced, I know that that is equal to the rate of change of magnetic flux, not maybe not equal, but let's say it is proportional, right? It's always proportional to the rate of change of magnetic flux through that coil. So, if I take this constant inside, what does that do? That I can write like this. Let's use the same color. So, okay, let's just rub it over here and add it. It looks like this. Okay. Now, the good thing here is I can equate, I can equate this, this quantity right here with flux. And when I do that, I get flux. This is equal to MOI, mutual inductance of outer with respect to inner multiplied with the current, multiplied with the current in the inner solenoid. Okay. Now, I'm interested in this thing right here, the mutual inductance. So, let's take current to the left hand side and when we do that, the mutual inductance, this is really, this is really equal to flux, flux divided by the current, flux divided by the current in the inner solenoid. And I can write this mutual inductance of the outer with respect to the inner. And also, when we talk about flux, because we are only looking at the outer solenoid for now, we can write this outer. Now, the good thing is that this is equal, right? So, when you are writing MO, you can write flux inner divided by the current in the outer. Now, we know that the current is increasing. So, when the current, this current increases, as a result of that, the strength of the magnetic field lines increase, which increases the flux. So, if you increase the current, that proportionally increases the flux. If you double the current, it will double the flux. And increasing the current in the inner solenoid really is increasing the strength of the magnetic field lines passing through the inner solenoid. But they are also passing through the outer solenoid, right? The inner one is inside the outer one. So, when you increase the current, the flux increases proportionally. And nothing really happens to the mutual inductance. Mutual inductance, in fact, remains the same. So, that's about it. Increasing the current increases the flux proportionally. And that doesn't change the mutual inductance. All right. You can try more questions from this exercise in the lesson. And if you're watching on YouTube, do check out the exercise link, which is added in the description.