00:01
In this question, we are going to determine the current induced in a coil that exists within the magnetic field of a solenoid whose current is changing.
00:14
So that's the key thing here is that the changing current for our solenoid is going to create a changing magnetic field from the solenoid.
00:28
And that changing magnetic field from the solenoid is going to induce an emf.
00:39
And then, of course, we can use ohm's law that the induced emf will be equal to the induced current multiplied by the resistance in order to get the current that we're looking for.
01:01
So let's mark out the two key things that we're going to need we are going to need first and foremost the fact that the magnetic field of a solenoid is given by mu naught times lowercase n times the current in the solenoid where lowercase n is the turns per unit length notice that we we were given turns per centimeter so we need to turn that into turns per meter by multiplying by 100 because there are 100 centimeters in a meter and then the second key thing that we are going to need for this question is of course going to be faraday's law that our the absolute value of our induced emf will be equal to the absolute value of minus capital n, where capital n is the number of turns in our coil, times the rate of change of magnetic flux.
02:08
So delta phi b over delta t.
02:13
And we will flesh that out a little bit later.
02:20
So let's start off with our solenoid here.
02:27
So i'm going to call it b1 will be equal to mu naught n times i1 so four pi sorry four pi times ten to the minus seventh multiplied by our 14 000 turns per meter multiplied by i1 with zero amps means that when when there's no current, we are initially starting off with no magnetic field.
02:55
And then b2, the field at the later time inside our solenoid, will be mu -naught n times i2.
03:03
So 4 pi times 10 to the minus 7th multiplied by 14 ,000 turns per meter multiplied by 3 amperes gives me 5 .278 i like to keep a few extra decimal places until i'm done calculating 5 .278 times 10 to the minus second teslas so that is how our magnetic field changes and then like like we said.
03:35
So because we have a changing magnetic field, the field of the solenoid is uniform throughout the interior of the solenoid.
03:43
So that means we have a changing magnetic field inside our coil.
03:46
The changing field inside the coil creates a changing flux.
03:50
And then that is what ultimately induces the cmf.
03:55
So let's come back to faraday's law step 2 here...