The figure below shows two current segments The lower segmen

The figure below shows two current segments. The lower segment carries current i_1 = 0.40 A and includes a circular arc with radius 6.6 cm, angle 180degree, and center point P. The upper segment carries current i_2 = 2i_1 and includes a circular arc with radius 4.9 cm, angle 120degree, and the same center point P. What are the (a) magnitude and (b) direction (into or otherwise of the page) of the net magnetic field B for the indicated current directions? What are the (c) magnitude and (d) direction (into or otherwise of the page) of B if i_1 reversed? (a) Number Units (b) (c) Number Units (d)

Solution

(a)
expression for magnetic field:
    B = _o i / 4 R
net magnetic field:
    B = [4*10^-7* (0.40 A) ( rad)/ 4 (0.066 m)] k^ - [4*10^-7*(0.80 A) (2 / 3 rad) / 4 (0.049 m)] k^
       = -1.5x10^-6 T

magnitude: 1.5x10^-6 T
(b)
     the direction is -k^ or into the page
(c)
the net magnetic field:
    B = - [_o (0.40 A) ( rad)/ 4 (0.066 m)] k^ - [_o (0.80 A) (2 / 3 rad) / 4 (0.049 m)] k^

       = - [4*10^-7* (0.40 A) ( rad)/ 4 (0.066 m)] k^ - [4*10^-7*(0.80 A) (2 / 3 rad) / 4 (0.049 m)] k^
       = -5.32x10^-6 T

magnitude: 5.32x10^-6 T
(d)
     the direction is -k^ or into the page