Figure $1$: A loop of current creating a magnetic field at the point P

Consider the loop of current shown in figure $1.$ It carries a current, I, has radius $\text{'}$a$\text{'},$ and is located in the yz plane.

$($a$)$ Calculate the magnetic field magnitude at a point P $,$ a distance x away from the center of the circle. This is known as an 'axial distance' from the center of the circle of current. $($HINT: Remember that even if the magnetic field vector at P points in an arbitrary direction due to dvec$(s),$ there is a radial symmetry due to the current travelling in a circle.$)(6$ points$)$

$($b$)$ What is the direction of the net magnetic field from the whole circle of current? $(2$ points$)$

$($c$)$ What if there is a charge moving in the hat$(i)$ direction with velocity $v_0$ at the point P $,$ what is the force on this particle? $(2$ points$)$