(20 points) A long insulated wire carries current I from left to right. As shown in the figure, the wire makes a circular loop of radius R in the middle. y I X R I I (a) (5 points) Using Ampere's law, derive an expression for the magnetic field (magnitude and direction) at the center of the loop due to the straight wire. Be sure to include a sketch of the Amperian loop you used. (b) (5 points) Derive an expression for the magnetic field (magnitude and direction) at the center of the loop due to the circular loop of radius R. (c) (10 points) If the loop is rotated 90 as shown in the figure, what is the direction of the net magnetic field with respect to the x-axis?