Can someone explain these equations?

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Discussion Overview

The discussion revolves around the interpretation and explanation of equations 196 and 197 from a physics lecture, focusing on vector relationships involving electric and magnetic fields. The scope includes conceptual clarification and mathematical reasoning related to vector sums and properties in the context of electromagnetism.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Main Points Raised

  • One participant describes equation 196 as expressing velocity as a vector sum of the ExB term and another vector v', noting the perpendicularity of the E and B fields.
  • Another participant explains that equation 196 can be understood by recognizing that any two vectors can be expressed in terms of each other, emphasizing the distinct properties of the ExB and v' vectors.
  • There is a challenge regarding the validity of equation 196, with a request for further explanation on why it holds true.
  • A participant suggests that separating the vectors allows for easier manipulation and understanding of their individual properties.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the validity of equation 196, with some providing explanations while others seek further clarification. The discussion does not reach a consensus on the foundational reasoning behind the equation.

Contextual Notes

The discussion does not address specific assumptions or definitions that may be necessary for fully understanding the equations in question.

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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.
 
Thanks. But why is equation 196 true?
 
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.
 
Oh, ok. That makes much more sense. Thanks!
 

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