$($a$)$ The figure below shows two parallel conducting rails $18\mathrm{.}4$ cm apart, connected by a resistor with resistance $R_3=5\mathrm{.}00.$ Two metal rods with resistances $R_1=10\mathrm{.}2$ and $R_2=15\mathrm{.}0$ slide along the rails with negligible friction. Rod $R_1$ slides to the left at constant speed $v_1=4\mathrm{.}00\frac{m}{s},$ while rod $R_2$ slides at speed $v_2=2\mathrm{.}00\frac{m}{s}.$ The rods and rails are in the presence of a uniform magnetic field pointing into the page, perpendicular to the plane of the rails, with a magnitude of $B_{in}=0\mathrm{.}0100T.$

$($i$)$

What are the magnitude $($in $A)$ and direction of the current through resistor $R_3?$

magnitude $$ IA

direction $$

$($b$)$ What If$?$ What are the magnitude $($in $A)$ and direction of the current through resistor $R_3$ if the rods move inward, instead of outward, with the same speeds as in part $($a$)?$

magnitude $A$

direction