00:01
Hello learners, in this question, we are given a sphere which is uniformly charged with the charge density of row and it is rotating with an angular velocity or angular frequency of omega.
00:16
We consider that there is a certain ring here, right here.
00:23
We consider this ring and take the distance from the center to this ring as r.
00:29
Then from the axis of the ring to its circumference, we'll have r sine theta, where theta is the angle here.
00:38
And the width of the ring, the little width of the ring is dr.
00:44
And here we have d theta, which is the angle between the little width of the ring.
00:51
So we can find the volume element of the ring as let's write here volume element.
00:58
And we denote this by dv is equals to 2 pi r which is the circumference that the ring multiplied with r sine theta d theta d t r now this gives us the volume element of the ring then the charge contained in the volume element charge contained in dv now this will be equals to row times dv because row is the charge density.
01:41
Now we can find the current in ring, current in the ring, and we'll call it d -i, which is equals to the frequency times charge -sensity multiplied with the volume element.
02:02
Here frequency, that is f is equals to omega, which is the angle of velocity divided by 2 -5.
02:13
This f is frequency.
02:15
So we can write d -i is equals to omega divided by 2 pi multiplied with row, multiplied with 2 by r squared, sine theta, d -teta, d -r.
02:36
Now since we have to find the magnetic field, let's look at the general case of how a ring puts magnetic field at the center.
02:51
Let's consider this figure.
02:52
Here, this dotted line is a ring in which occurrence flows, and the distance of this dotted line from the center is r as was in our sphere...
