Question $3(35\%)$

A point particle $q$ that has charge $=1{10}^{6}C$ moves at a velocity $=2\frac{m}{s}$hat$(y)$ along the line $x=-3m$ in the $x$ y plane as shown:

Assume at time $t=0,$ the charge q is at $x=-3m,y=1m.$

a$)$ What is the vector vec$(r)$ connecting the charge $q$ to the point of measurement $O?$

b$)$ What is the unit vector hat$(r)$ along that vector?

c$)$ Using the formula for the magnetic field due to a moving charge, find the magnetic field at point $0$ due to the charge $q$ at time $t=0.$

d$)$ Find the magnetic field due to the charge $q$ at time $t=1s($Hint: where is $q$ at $t=1s?).$

e$)$ What is the magnetic field at point $O$ when the charge $q$ is at $y=+?$