Using Lorentz Force Equation to find kinetic energy of a particle.

[Vagabond7]

Homework Statement

A charged particle (m=1.673*10^-27 kg) exists in a region with E=10 kV/m in the x direction and B=1T in the y direction. If the particle moves without being deflected calculate its kinetic energy.

Homework Equations

F=Q(E+u x B) and KE=1/2 mu^2 where u is velocity.
This is an upper level Emag course so we use multivariable calculus, differential equations and linear algebra, so any techniques using these things are fair game.

The Attempt at a Solution

Ok, I know I need to solve for velocity in order to find the kinetic energy, but I do not know how to get there. I can't deduce it from the cross product because I am not told what direction the velocity is in. Even though the mass of the particle is that of a proton, I'm feel like the are omitting this fact so that I don't use charge for anything. I don't know what the force is, so I don't know what the acceleration is, so I can't use acceleration to deduce anything. Plus, the answer is just a constant so I guess it isn't accelerating or else the kinetic energy would increase as the velocity increases. I'm not sure how to go about this.

Also, I admit my understanding around the lorentz force equation is admittedly shaky, so any intuition as to what is happening here is appreciated. It seems like if there is a charged particle in an electric field it should be experiencing a force. But they aren't giving me charge, so it seems like it must not be an important detail. Any hints or pointing me in the right direction would be much appreciated.

 

[Vagabond7]

Lolz, never mind I solved it. I swear, I should write my question then wait ten minutes. Writing the question always helps.

Oh, in case anybody else needs a hint on a problem like this one. The identity u x B = the magnitudes of u*b sinθ helps. Allows for a more algebraic solution.

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