Two horizontal electrical plates are placed $25$ cm apart, with the positive plate on top. When turned on$,$ the plates exert a potential difference of $15\mathrm{.}0$ V $.$

a$)$ When an electron is positioned halfway between the plates and the plates are turned on$,$ what is the electrostatic force it experiences?

b$)$ What is the net force it experiences?

c$)$ What is the acceleration it experiences?

Suppose that the ion source in a mass spectrometer produces doubly ionized gold ions $(A{u}^{2+}),$ each with a mass of ${3\mathrm{.}2710}^{-25}kg.$ The ions are accelerated through a potential difference of $1\mathrm{.}00$ kV $.$ Then, a $0\mathrm{.}500$ T magnetic field causes the particle to follow a circular path. What is the radius of the path of the particle? $(3$ marks$)$

A square coil of wire is placed in a uniform $0\mathrm{.}25$ T magnetic field, as shown. Each side has a length of $0\mathrm{.}32$ m $,$ and the current in the coil is $12$ A $($directed clockwise$).$ Determine the magnitude and direction of the force on each of the four sides of the loop. $(2$ marks$)$