00:01
Hello everyone in this problem it is given there is a solid sphere of radius r and having volume char density row this is the center r is the radius of it row is the volume char density we have to calculate magnetic field intensity at the center of it when it is to be rotated with angular velocity omega to solve this problem we will consider a ring at a position position x so this distance is x from the center of the sphere its radius is r so this radius is r its thickness is d x and width is d r so this is the elemental ring of radius small r at a position x from o that is center of the sphere having volume to a density now we will find the charge on elemental ring.
02:05
This would be volume charge density into volume of it.
02:12
Volume will be 2 pi r, d r, this is the area into its thickness that is d x.
02:24
So this is the ring and we know that on the axis of the ring magnetic field intensity is mu not, d .i.
02:39
That is the current due to rotation of the sphere through the ring r squared divided by 2 r square plus x squared to the power 3 by 2 now value of dq you know so current flowing through this ring will be dq omega by 2 pi now dq is 2 pi r, dr, dr and d x divided by 2 pi.
03:27
So this value can be written as r, dr, dx into omega.
03:46
Substitute this value in equation 1.
03:54
So magnetic field at the center of the solid sphere, due to this ring element would be mu not, ro omega, r cube, d r, d r, d r, d r, d...