Analysis of Lorentz Force on Particle Motion

AI Thread Summary
The discussion focuses on analyzing the Lorentz force acting on a charged particle in electric and magnetic fields. The total force is expressed as F=q(E + vxB), where v is the particle's velocity. Participants suggest using Newton's second law (F=ma) to derive the relationship ma·v = qE·v through dot products. The challenge lies in simplifying the equation after distribution, particularly with the term q(vxB). The conversation emphasizes the importance of vector identities in this simplification process.
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Homework Statement


Consider a particle of mass m that carries a charge q. Suppose that the particle is under the influence of both an electric field E and a magnetic field B so that the particle's trajectory is described by the path x(t) for a\leqt\leqb. Then the total force acting on the particle is given in mks units by the Lorentz force,

F=q(E + vxB),

where v denotes the velocity of the trajectory.

a) Use Newton's second law of motion (F=ma) to show that

ma.v = qE.v (dot products)

Homework Equations





The Attempt at a Solution


Tried distributing to help make sense of the problem, but didn't do much for me:
ma = qE + q(vxB)

 
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veritaserum20 said:
Tried distributing to help make sense of the problem, but didn't do much for me:
ma = qE + q(vxB)

Take the dot product of your equation with v and use an appropriate vector identity to simplify it.
 

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