A wire with linear density $($mass per unit length$)$ of $1$ gram$/$cm is placed on a horizontal surface with a coefficient of kinetic friction of $0\mathrm{.}20.$ The wire carries a current of $1\mathrm{.}50$ A eastward. In a vertical magnetic field, the wire moves horizontally to the north with a constant speed of $4\mathrm{.}2$ m$/$s$.$ a$)$ What is the magnitude of the vertical magnetic field that enables the wire to move in this fashion? b$)$ If the coefficient of kinetic friction becomes $0\mathrm{.}80$ and current becomes $3\mathrm{.}0$ A$,$ what is the magnitude of the magnetic field acting on the electrons$/$current$?$

a$.$ Answer: $\_\_\_\_\_\_\_\_\_\_\_$

b$.$ Answer: $\_\_\_\_\_\_\_\_\_\_\_$