00:01
Hi, here in this given problem there is a rectangular loop.
00:06
Suppose this is the loop a, b, c and d.
00:14
Its sides are given as the smaller site that is a is equal to 0 .3 meter and longer site that is b is equal to 0 .8 meter.
00:30
Current passing through this rectangular loop in clockwise direction that is 7 .6 ampere.
00:44
Now we have to find net magnetic field at the center of this rectangular loop.
00:55
So this is the center.
00:58
We have to find net magnetic field here and there will be four magnetic fields due to the four arms.
01:10
These distances here, distances of the observation point from the longer sides will be equal to a by 2, a by 2 each, and distances of the observation point from the longer side from the shorter sides will be equal to half of the longer side.
01:33
Means b by 2 and b by 2.
01:38
Now we know if we are having a finite length of current carrying conductor, then the magnetic field at a point distant r from it that is given as if these angles are known as alpha and beta, then the magnetic field expression is b is equal to mu not upon 4 pi into i by r into sine alpha plus sine beta.
02:19
So here we have to use that expression.
02:23
So first of all we will find these angles.
02:30
Suppose this is alpha and here this is b.
02:37
So, to find these angles first of all, an alpha will be equal to this b by 2 by a by 2 means this is b by a or we can say this is 0 .8 by 0 .3 means 8 by 3 which is 2 .7.
03:04
So, this angle alpha will be given by 10 inverse of 2 .67, or we can say this is 69 .4 degree.
03:18
Then for beta, 10 beta will be given by a by 2 by b by 2, means this is a by b, means 3, 0 .3 by 0 .8.
03:35
And it comes out to be equal to 0 .375.
03:40
So this angle beta will be given by 10 inverse of 0 .375 means this is 20 .6 degree.
03:52
So now using this expression as the magnetic fields due to all these four arms will be in the same direction and that is into the plane of paper...