biot savart

[eisley_90]

pls help me!! this is the question,a thin ring 10m is placed on plane z = -1m so that its center is at (0,0,-1m).If the ring carries 5A along -UØ ,find the magnetic field intensity at (0,0,2m)

 

[MrAl]

Hi,

To start you can adjust the coordinate system so that the center of the ring is at (0,0,0) and the point is at (0,0,3). That makes it slightly simpler.

Next, you can start with Biot Savart for a finite length of straight thin wire and generalize to a constant current and a constant radius R, with constant angle of 90 degrees. The angle is relative to the distance along the wire length (ring circumference) not along the radius of the ring so this angle is perpendicular to the wire. This greatly simplifies the whole problem and integration that comes next which really almost isnt even necessary. The radius R is obtained from the Pythagorean Theorem using the radius of the ring as one side and the distance from the center of the ring to the point of interest as the other side.

Next, Integrate over the circumference and then multiply by the required constants that appear in Biot Savart.

Next, compensate for the joining vector angles at the point by computing the scaling factor for the particular angles at which they meet. They dont meet in parallel so the resulting field will always be less than if they did such as at the very center of the ring in the same plane as the ring.

There are other ways to do this that are a bit more complicated. For example, in developing a formula for the field at any point along the axis of the ring instead of at just one point we would have to develop a formula that includes z explicitly and reduce as much as possible.

Also, dont mispronounce the name