Question

hello , this Electromagnetics class

i want the answe for all of these four questions please with clear picture and clear written and clear explantion.

The current carrying contour shown on right consists of 3 segments two of which are straight and the third being part of a circle of radius a. All segments are in the plane za and the two straight segments extend from/to infinity. The current Iflows in the direction shown (from x to y) The following problems (18 through 21) concem the Biot-Savart law and the magnetostatic field H, with the observation point being the origin O of the coordinate system shown. 18. For the I segment, which is parallel to the x-axis, what is df'xR? a) adx'y b) -adx c) adx' d) adx' e) None of the others 19. For the 2d segment, which is parallel to the y-axis, what is d'xR? a) adx' b) None of the others c)-ady d) -adx' e) ady' 20. For the 3d segment, which is the partial circle of radius a, what is d'x R? a) ad b)-d dp e) a'dø' d) None of the others e) a'dd-a'dp 21. For the 3nd segment, which is the partial circle of radius a, what is the magnetic field H at the origin? a) None of the others b) m 16 ]A/m e' d) e) 0 A/m

Answer 1

M^rightarrow = integral uIdl sin 90 degree/4 pi (squareroot 2a)^2(sin 45 degree) Z - integral uIdl/4 pi (squareroot 2a)^2 cos 45 degree - u_0Idl/4 pi (squareroot 2a)^2 cos 35 degree sin phivariant X \r\n M^rightarrow = integral^pi/2_0 u_0/4 pi I a d phivariant/2a^2 1/squareroot 2 Z - integral^pi/2_0 u_0 I a d phivariant/4 pi 2a^2 1/squareroot 2 cos phivariant Y - integral^pi/2_0 u_0 I a d phivariant/4 pi 2a^2 squareroot 2 sin phivariant X u_0/8 Ia/2a^2 1/squareroot 2 Z - u_0/4 pi Ia/2a^21/squareroot 2[X + Y] B^rightarrow = u_0 I/16 squareroot 2 a Z - u_0I/8 pi asq 2[X + Y] dl^rightarrow times R^rightarrow for segment dl = -dx X R = a Z dl^rightarrow times R^rightarrow dl = dy Y R = a Z dl^rightarrow times R^rightarrow = a dy X \r\n dl^rightarrow times R^rightarrow dl = a d phivariant phivariant R = a r dl^rightarrow times R = a^2 d phivariant - P