$*$Please help with parts e$,$ f$,$ g and h only!$*$ Solutions are attached, please give detailed response! $VN-2$ a$)5\mathrm{.}27{10}^{13}\frac{m}{s^2}(-$hat$(i))$

b$)$ zero

c$)1\mathrm{.}76{10}^{15}\frac{m}{s^2}(+$hat$(k))$

d$)$ A circle with its center on the $z$ axis to the left of the origin.

e$)$ A spiral $($with the same radius as the circle$)$ going to the left with increasing spacing between the turns.

f$)T=\frac{2(m)}{qB},T=1\mathrm{.}43{10}^{-10}s.$

g$)-7\mathrm{.}54{10}^3\frac{m}{s}$VN$-2$ A magnetic field $B=0\mathrm{.}250T$ points in the $+$x direction. An electric field $E=3\mathrm{.}00{10}^2\frac{N}{C}$ also points in the $+$x direction. An electron has an initial velocity $V=4\mathrm{.}00{10}^4\frac{m}{s}$ in the $+$y direction when it is at the origin as shown below.

a$)$ Find the acceleration $($magnitude and direction$)$ of the electron in the x direction when the electron is in the position shown above.

b$)$ Find the acceleration $($magnitude and direction$)$ of the electron in the $y$ direction when the electron is in the position shown above.

c$)$ Find the acceleration $($magnitude and direction$)$ of the electron in the z direction when the electron is in the position shown above.

d$)$ Sketch the path of the electron as seen looking down the $+$x axis at the origin $($the view above on the right$).$

e$)$ Sketch on the figure on the left on the first page the path of the electron.

Show $3$ or more $($a minimum of $3)$ revolutions.

f$)$ Starting with Fnet$-$ma applied to the electron, find the symbolic equation for the next time at which the electron is at a position with $y=0$ and with the y component of the velocity pointing upward.

g$)$ Use your equation from f$)$ to find the numerical value for the next time at which the electron is at a position with $y=0$ and with the $y$ component of the velocity pointing upward.

h$)$ Find the $x$ component of the velocity after the time you foVN$-2$ A magnetic field $B=0\mathrm{.}250T$ points in the $+x$ direction. An electric field $E=3\mathrm{.}00{10}^2\frac{N}{C}$ also points in the $+$x direction. An electron has an initial velocity $V=4\mathrm{.}00{10}^4\frac{m}{s}$ in the $+$y direction when it is at the origin as shown below.

a$)$ Find the acceleration $($magnitude and direction$)$ of the electron in the $x$ direction when the electron is in the position shown above.

b$)$ Find the acceleration $($magnitude and direction$)$ of the electron in the $y$ direction when the electron is in the position shown above.

c$)$ Find the acceleration $($magnitude and direction$)$ of the electron in the z direction when the electron is in the position shown above.

d$)$ Sketch the path of the electron as seen looking down the $+x$ axis at the origin $($the view above on the right$).$

e$)$ Sketch on the figure on the left on the first page the path of the electron. Show $3$ or more $($a minimum of $3)$ revolutions.

f$)$ Starting with Fnet$=$ma applied to the electron, find the symbolic equation for the next time at which the electron is at a position with $y=0$ and with the y component of the velocity pointing upward.

g$)$ Use your equation from f$)$ to find the numerical value for the next time at which the electron is at a position with $y=0$ and with the $y$ component of the velocity pointing upward.

h$)$ Find the $x$ component of the velocity after the time you found in part f$).$und in part f$).$