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I got this question off mastering physics and was unable to understand it. I eventually gave up to concentrate on other assignments and asked for the answer. I was unable to come up with more than one answer I thought possible without resorting to trial and error.

Answer: V_{x},V_{y},V_{z}= 0,-234,0 m/s

1. The problem statement, all variables and given/known data

A 6.50 negative microC particle moves through a region of space where an electric field of magnitude 1200 N/C points in the positive x direction, and a magnetic field of magnitude 1.02 T points in the positive z direction.

If the net force acting on the particle is 6.25×10^{−3 }N in the positive x direction, find the components of the particle's velocity. Assume the particle's velocity is in the x-y plane.

V_{x}= ? V_{y}=? V_{z}= ?

2. Relevant equations

Force = electric field * charge

or F=e*q

Force = magnitude of charge * velocity * magnetic field * sin tither

or F=|q|*v*B*sin tither

3. The attempt at a solution

Force on particle due to Electric Field = E*q

= (1200N/C)(-6.5*10^{-3}C)

= -7.8*10^{-3}N

Force on charge due to magnetic field = |q|*v*B*sin tither

= (6.5*10^{-6}C)(1.02T)(v)(sin 90)

= (6.63*10^{-6})(v)

F_{x1}along x axis = -7.8*10^{3}N

I'm sure the force on charge due to magnetic field lies between axis of positive Y and axis of negative X. The force on the particle needs to be perpendicular to the positive z direction of the magnetic field and the velocity of the particle which is one the x-y plane. Since the net force is in the x-direction, it should be along the x-axis. This was also the reasoning that led me to using sin90 when determining the force on the charge due to the magnetic field.

F_{x2}along x axis = (6.63*10^{-6})(v)

At this point, I thought I understood the problem statement fully. I took the net force from these two vectors I had come up with and seperated velocity to LHS and the constants to the right.

V_{x}= (Net Force x + F_{x1}) / (F_{x2}without velocity term)

= ((6.25×10^{−3 })+(7.8*10^{3})) / (6.63*10^{-6})

= 2.12*10^{7}m/s

The value was ridiculously large and I was not surprised it was rejected by mastering physics. I think I have a huge misunderstanding of the concept or method behind this question. Please explain to me how I should go about dealing with a question of this type or point out my mistakes. I do not need a worked out solution, coming up with that myself would probably be better for me.

Thank you

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# Initial velocity of a charged particle acted upon by magnetic and electric fields

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