Question $3$: $(35\%)$

Consider a current carryine loop in the $x-y$ plane as shown $($cenetered on $x,y,z=0)$ with a $10$ cm radius. carryine a current of $1$ amperes, $1$ is counter$-$clockwise looking from the top.

a$)$ What is the value of the magnetic field at The origin $O?$

b$)$ Assume a ring of radius $R=20cm$ is concentric with the ring above. What is the current that needs to run in that ring and what is its direction for the field at $O$ to be exactly $0?$

c$)$ What is the electric field at $O$ due to the ring? Explain.