the cross product of B and v would be the product of their magnitudes and sine of the angle between them. This will result in a vector with a direction normal to both B and v (right hand rule).
Yes, essentially what you need to do is add the two forces together.
hello
here's the paper.
http://www.physics.utah.edu/~rprice/00_2220/collab10.pdf
for the first part am i right in assuming that E flux is present only through the LH faces?
and that i need to double integrate E first with respect to x from zero to L and then with respect to z fom 0...