Based on Example $1\mathrm{.}13,$ answer the following questions:

$($a$)$ Considering two unknown vector fields $E$ and $B($total $6$ scalar components$),$

can we use two tests of V$1$ and V$2$ with the measured forces F$1$ and F$2$ to

uniquely determine unknown fields $E$ and $B?$ If not, make a brief explanation.

If yes, write down the method $($algorithms or procedures$)$ of your thought.

$($b$)$ Repeat $($a$),$ if we add a constraint to the E$-$B relationship that E$-$field is

perpendicular to B$-$field, then whether the problem is solvable now? If still not,

why not? If yes, write down your solution algorithms$/$procedures$.$

$($c$)$ Repeat $($b$),$ find the velocity $V$ that makes the test charge pass through the field

zone un$-$affected without any deviation.

$$ This problem was inspired by StarWars. $>>>$