Can someone explain these equations?

1. Jun 11, 2014

pierce15

2. Jun 11, 2014

Staff: Mentor

equation 196 is just saying that v can be written as a vector sum of ExB/b^2 + v'

the ExB vector is perpendicular to both E and B fields (which in this case are perpendicular to each other)

and so subbing the expression in for v into equation 195 you get equation 197

vxB = (ExB/B^2 + v') x B = ExBxB/B^2 + v'xB = v'xB since ExBxB is zero vector.

3. Jun 11, 2014

pierce15

Thanks. But why is equation 196 true?

4. Jun 11, 2014

AlephZero

If you have any two vectors p and q, you can always write p = q + v'. v' is just p-q.

The reason for doing this in Eq 196 is because the ExB vector and the v' vector each have different "nice" properties, and after you split up the equation you can work with each vector separately.

5. Jun 11, 2014

pierce15

Oh, ok. That makes much more sense. Thanks!