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Okay, one thing that we just talked about was the following. Let's say that I have a coil, and I'm going to take a bar magnet, and I'm going to push it towards the coil. When I do that, I can generate an epsilon in the coil. Okay, but pushing the bar magnet towards the coil is really like increasing the strength of the magnetic field in the coil. So let's replace the bar magnet with a solenoid. So let's take a solenoid right here, and we're gonna run some current through the solenoid. And if I run current I through that solenoid I know what it's gonna do. It's gonna produce a B field that is pointing up, just like the B field was pointing up over there. And if I increase the current going through this thing I'm going to increase the strength of the B field, and that is also going to generate an EMF in the coil. And, in fact, we know what direction it is, if B is increasing going up, then the coil is going to want to oppose that, and so it's going to have a current in the opposite direction. And now here's the cool thing, right? Let's call this current in the solenoid a primary, and let's call this one the secondary. Okay, but is there any reason that I just need to have one coil there? No, not at all. I can do many coils up there. But let's think about the following. Instead of doing that, right, let's do just one coil to simplify everything. So I'm gonna make one coil like so, and it's gonna come back around and we're gonna call that our secondary coil. And then down here I'm gonna have a primary coil, wraps around. And we're gonna run current through these things. If I run current, I'm gonna intercept some flux. And the amount of flux that I intercept in the secondary depends on how much current I run through the primary. And so this is equal to M times Ip. This is IP, there's some current Is which develops in the top one. How much current depends-- how much current in the bottom one dictates how much magnetic field is gonna go through the top one. And so you get this factor M in there, where M is something called the mutual inductance. And now we're going to go back to this case where we add many turns to it. So in my secondary if I put many turns, then the amount of flux just increases like N. So with Ns turns, then the flux goes like N, but that is still just equal to M times IP and so you can write down what M is. M is equal to N sub s phi sub s divided by I sub P. Okay, but Faraday told us that if you're intercepting flux and it's changing in time, then you develop an EMF. The EMF we said was minus N delta phi over delta t. And so in the secondary, the EMF which develops is minus N sub s delta phi sub s over delta t. But we know what n sub s phi sub s is. And so this becomes minus delta M I sub p divided by delta t, and we get an equation for the EMF and the secondary. It is minus M change in the primary current delta Ip divided by delta t. Okay, so coils can, in fact, talk to each other. Run current through the lower coil, there is current that is generated in the upper coil. How much? Well this is the EMF that defines it.

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