For the following problem utilize BiotSavart a For the curre

For the following problem, utilize Biot-Savart. a. For the current paths shown below, determine the expression of themagnetic point P. Manipulate your expression until all unit vectors are removed from the intergal (s) Do not execute the integral(s)!

Solution

The sides will not contribute because the cross product is zero there. So using

the Biot-Savart Law we have that,

Direction Of Field From the Left Hand Rule , Outside of the Plane of XY , that means Positive Z direction ( +Z)

arc (r ) =_o/4 Ids × ˆr / r²

         =     +z   _o/4   Ids × ˆr / R²      ds

         =    +z   _o/4   I ˆr / R²    1/4(2R )       // After integration of 1/4 of loop

         =    +z   _o/4   I ˆr / R²    1/4(2R )       

          =       +z _o I       (  1/4) (   1 /4 ) ( 2R/   R²   )      // rearranging whole eqation

          =     +z _o I  (1/8R)     

Where    + Z is direction  

           _o is Permiability

            I   is currennt

           R is   Radius

For this Example Radius is a, so

=     +z _o I  (1/8a) will be the answer

Answer B : only path of ARC will contribute in Fields ,

Current going away from the Point P on X axis will not Contribute, because the cross product is zero there.

As there will be change in distance which will change the effect of field at each point and is come to zero as the is variable integral will come with out put zero,

it is important to have Arc and movement in radius to make field.