00:01
Here in this portion we are given a regular hexagon.
00:03
Hexagon is representing a polygon which is having six sides.
00:08
So this is a regular hexagon shaped wire loop with a side of length let's say side is given which is equals to 25 .9 centimeter which carries a electric current which is represented by i that is equals to 17 .6 ampere.
00:24
So we have to determine the size of the magnetic field at the center of the hexagon in the first part.
00:29
So here what we can say that we are having the value of i and side.
00:35
So what we can do in the first part of the quotient let's say this is basically the case here we are having this side let's say this a regular hexagon is this angle is 60 degree and from here if we can do this this complete angle is 90 degree so the remaining angle this from here is 30 degree.
00:55
So from here as from here we can say that let's say this distance from this point let's say this is point a point b c d e and point f.
01:07
So the distance let's say this is x and this distance from here is c and let's say this is y.
01:13
So from here we can say that x is equals to a sin of 30 degree and we know that the value of sin 30 is 1 divided by 2 so value of x become equals to a divided by 2.
01:25
In the same way z become equals to a cos of 30 degree and the value of cos 30 is under root 3 divided by 2 so the value of z become equals to a multiplied by the under root 3 that is divided by 2.
01:38
So from here what we can see that that the magnetic field due to ab is equals to magnetic field due to the side ed.
01:48
So from here magnetic field is given by the formula that is equals to mu naught i which is divided by the 4 pi r multiplied by the angle sin of minus 30 degree plus sin of 60 degree.
02:04
So plugging to the value that become equals to mu naught i which is divided by 4 pi multiplied by the r multiplied by the under root 3 minus 1 which is divided by 2.
02:14
So this from here is equals to mu naught i which is divided by 4 pi multiplied by the a multiplied by the under root 3 which is divided by 2 this is further divided by under root 3 minus 1 which is divided by 2.
02:27
Now if we plug in to the value here that become equals to pi mu that is equals to 4 pi multiplied by the 10 raised to the power minus 7 which is further multiplied by the 11 .2 ampere which is divided by 4 pi multiplied by the 0 .258 which is further multiplied by the under root 3 minus 1 which is further divided by under root 3.
02:48
Further when we simplify this term we get the value of magnetic field that become equals to 1 .833 multiplied by the 10 raised to the power minus 6 tesla.
02:57
So this is the answer to the part a of the question this is the size of magnetic field at the center...