|Jan28-04, 06:16 AM||#1|
can someone explain this to me?
The force acting on a moving charge particle with mass m and charge q in a magnetic field B is the Lorentz force F= q(v x B), where v is it's velocity. Suppose thata particle moves in the (x,y) plane with a uniform B field in the z direction. Assuming Newton' second law, mdv/dt = F, show that the forceand velocity are perpendicular, and that both have constan magnitude. Hint: Find (d/dt)(v dot v).
I don't know where to start. How do you take the derivative of v dot v?
|Jan28-04, 07:45 AM||#2|
I suspect this will be moved to the "homework" section!
You differentiate v dot v using the "product rule":
The derivative of v dot v is: dv/dt dot v+ v dot dv/dt. Since the dot product of vetors is commutative, this is the same as 2v dot dv/dt (should remind you of the derivative of v2).
Since you are told that "the Lorentz force F= q(v x B)
"mdv/dt = F" becomes m dv/dt= q(v x B)
|Feb1-04, 01:46 PM||#3|
I think you should take the dot product first, then take the derivative....it is easier to see what is being done and the algebra is simpler.
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