Can someone explain these equations?

[pierce15]

Hello,

Can someone explain what's going on in equations 196 and 197: http://farside.ph.utexas.edu/teaching/336k/lectures/node30.html#e5.23

Thanks.

 

[jedishrfu]

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.

 

[pierce15]

Thanks. But why is equation 196 true?

 

[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.

 

[pierce15]

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