A rectangular coil with resistance $\backslash ($ R $\backslash )$ has $\backslash ($ N $\backslash )$ turns, each of length $\backslash (\backslash$ell $\backslash )$ and width $\backslash ($ w $\backslash )$ as shown in the figure below. The coil moves into a uniform magnetic field $\backslash (\backslash$overrightarrow$\{\backslash$mathbf$\{$B$\}\}\backslash )$ with constant velocity $\backslash (\backslash$overrightarrow$\{\backslash$mathbf$\{$v$\}\}\backslash ).$ What are the magnitude and direction of the total magnetic force on the coil for the following situations? $($Use the following as necessary: $\backslash ($ N$,$ B$,$ w$,$ v $\backslash ),$ and $\backslash ($ R $\backslash ).)$

$($a$)$ The coil enters the magnetic field.

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$($b$)$ The coil moves within the field.

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$($c$)$ The coil leaves the field.

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