$1.$ A $5$ nC charge is moving in the positive $\backslash ($ x $\backslash )-$direction with a velocity of $\backslash (2500\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$s$\}\backslash ).$ It it traveling while inside a uniform magnetic field of $0\mathrm{.}25$ T that is pointing in the positive $\backslash ($ y $\backslash )-$direction. What is the work done by the magnetic field on the particle? If we assume the mass of this particle is the proton mass, how does its kinetic energy change from $\backslash ($ t$=0\backslash$mathrm$\{$~s$\}\backslash )$ to $\backslash ($ t$=5\backslash$mathrm$\{$~s$\}\backslash )?$

$-$ Hint: First write out what work is$.$

$2.$ An proton moves with a velocity of half the speed of light inside a uniform electric and magnetic field. It's velocity is in the positive $\backslash ($ x $\backslash )-$direction. The electric field is also in the positive $\backslash ($ x $\backslash )-$direction and has a magnitude of $\backslash (10^\{\backslash$wedge$\}6\backslash$mathrm$\{$~V$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The magnetic field is directed in the positive $\backslash ($ y $\backslash )-$direction $($into the page$)$ and has a strength of $2$ T $.$

$-$ Draw a diagram of this system. Clearly label all quantities.

$-$ Calculate the net force on the proton just as it enters this region of electromagnetic field.

$-$ Describe $($in words$)$ the motion of this particle as it moves through these two fields. Think very carefully about the freebody diagram as the charge moves.