$[12$ Points$]$ A conductor in the shape of a square loop of edge length $L$ carries a current I as shown in the figure. Notice that the current flows clockwise around the loop.

a$.$ What is the direction of the magnetic field at the center of the square? Circle ONE answer. $(2$ pts$)$

Up Down Left Right Out of the Page Into the Page

b$.$ Find the magnitude of the magnetic field at the center of the square. Express your answer in terms of some or all of the following: ${}_0,$I,$L.$ Hint: Find the magnetic field due to a current segment of length $L$ first. $(5$ pts$)$

$B_{\text{s}\text{q}\text{u}\text{a}\text{r}\text{e}}=$

c$.$ If this conductor is formed into a single circular loop and with the same current, what would the magnetic field be at the center of the loop? Express your answer in terms of some or all of the following: ${}_0,$I,$L.(5pts)$

$B_{\text{r}\text{i}\text{n}\text{g}}=$