Answer
$B = 0.10~T$
The positive charges are on the left and the negative charges are on the right.
Work Step by Step
We can find the magnetic field strength:
$emf =B~L~v$
$B =\frac{emf}{v~L}$
$B =\frac{0.050~V}{(5.0~m/s)(0.10~m)}$
$B = 0.10~T$
If the magnetic field is directed into the page, then there would be a force on a positive charge directed toward the left. By Lenz's law, a potential difference is induced which opposes this. Therefore, the positive charges are on the left and the negative charges are on the right.
