00:01
So this question we're told we have two solenoids.
00:03
One of them is a small one with radius r1, and we've got a big one with radius r2.
00:08
They both carry the same current, i, but they have different numbers of coils per unit length, n1 and n2.
00:15
And we're asked to find the magnetic fields b1, b2 and b3, which are inside both solenoids, between the solenoids and outside the solenoids.
00:26
So basically, what we're going to do is we're going to first, firstly, use the fact that we're going to use the fact that the magnetic field very far away from this thing is going to be zero.
00:41
And the fact that amper's law says that say we have a current loop, an amper's law loop here.
00:51
And if the current is zero here, it's enclosing no current here.
00:55
So the current must also be zero here.
00:57
So we can just say b3 equals zero.
01:00
That's our first equation.
01:01
So we've got now we can think of a second loop, a loop that goes in the middle, out here and this way.
01:17
And amper's law tells us that, so it has a length l.
01:22
Amper's law is that the integral around a closed loop of b .d .l is equal to mu -nought times the current enclosed.
01:30
So looking at this second loop, we're going to have b1 times l minus b2 times l is going to be equal to mu -nall times mune or times the current enclosed.
01:50
But the current enclosed here is going in the wrong direction.
01:57
So that means that because it's coming out of the page rather than going in, so that means that this is going to be minus mu -naut -n1 -l.
02:14
Yeah, so that's right...