00:01
In the equation, we are supposed to find the magnetic field at the center of the sphere and the magnetic movement of the sphere.
00:07
So we know, first of all, that dq is equals to 2 pi r, sine theta, multiplied by r delta t, row, which is equal to, we can say, 2 pi, row, r square, sine, theta, and d, and d .i is equal to, i'm sorry, omega dq, divided by 2 pi, since we know that, d .i is equal to d.
00:30
Dq divided by t and now which we can write as omega r square sine theta d theta let this be equation number one now for the a part the magnetic field at the center we know db is equals to mu not di r square sine square theta divided by two r q using equation number one theta is equal to integration of db so now we can say from here would be equal to the value of b it's b would be mu not omega are divided by 2 sine cube theta d theta and now the answer would be mu not omega row are divided by 2 integration of 0 to pi sine cube theta d theta and the integration of sine cube theta would be mu not omega row r divided by multiplied by sine 0 to 2 pi 5 divided by 2 5 divided by 2 sine cube theta b theta and when we solve this we get the value for b vector 2 divided by 3 mu not omega row r k vector since we know that sine cube theta is equal 2 x2 divided by 4 3 sine theta minus sine 3 theta and now for the b part we have the magnetic movement due to elementary ring which is dmue is equal to d i multiplied by pi r square so mu integration of this say from here that would be equal to integration of di multiplied by r r r r square and when we put the values into this we get two multiplied by integration zero to pi by two omega r square sine theta, pi r square, sine, theta, d theta...