00:01
Hi, here in this given problem there is a very long wire bent like this.
00:16
And then we have to find net magnetic field at a point midway between the two ends of this u -shaped wire.
00:32
This point is mark as p.
00:34
Here these lengths of the wire are a each current i is flowing through the conductor towards right so here it will be up again towards right down and again towards right we give name to these five segments as segment one segment segment 2, segment 3, segment 4 and segment 5.
01:13
So first of all, as this observation point t is such that the line joining the observation point with these current carrying conductors 1 and 5, it will be making a 0 degree angle with the conductors or we can say current element.
01:32
So there will be no magnet field at point p.
01:34
So magnetic field at p is 0 due to the current elements 1 and 5.
02:03
Now due to this current element 2, observation point is this at a distance a by 2.
02:12
So, if we join observation point from the upper end of this segment, vertical segment and to the lower end, this angle alpha, we should know this angle alpha, and the distance of the observation point a by 2, then magnetic field in magnitude 2 means magnetic field due to the current element 2, that will be equal to magnetic field due to the current element 4.
02:41
B2 should be equal to b4.
02:43
And using by 107s law that is mu not upon 4 pi, i by distance which is a by 2 into sine alpha plus sine beta.
03:00
Sin beta angle made by the observation point at the wire in front of it, that will be 0 degree.
03:10
So this is mu not upon 4 pi.
03:14
2 i by a and for sine alpha that is perpendicular which is a by hypotenuse means a by hypotenuse of this right angle triangle that is a square of a plus square of a by 2 which is a square by 4 so it will come out to be equal to mu not upon 4 pi into 2 i because this a will be cancelled and that is 5 a square by 4...