E$18$B$.6$ A proton is initially at rest. Suppose that at time $t=t_0=0,$ we accelerate it at a rate of ${10}^{16}\frac{m}{s^2}$ for $2$ ns in the $+z$ direction $($since the proton has such a small mass, such a large acceleration is realistic$).$ Afterward, the proton coasts in the $+z$ direction at a constant velocity. An observer at point $P$ that is $300$ m away from the proton in the $+x$ direction monitors the proton's electric field at that location. $($Note that it takes light ${10}^{-6}s$ to travel

$($a$)$ At $t_1=1\mathrm{.}0ns,$ what is the magnitude and direction of the electric field at point $P?$

$($b$)$ At $t_3=1001ns,$ what is the magnitude and direction of the electric field at point $P?$

$($c$)$ How do the results from parts $($a$)$ and $($b$)$ compare?

$($d$)$ What is the magnitude and direction of the magnetic field at point $P$ at time $t_3?$

$($e$)$ How much total electromagnetic energy did this proton radiate?

$($f$)$ Suppose that an electron was initially at rest at point $P$ at $t_2=1000ns.$ At time $t_3=1001ns,$ what are the directions of both the electric force and the magnetic force acting on the electron?