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

1. Nov 11, 2014

### Vagabond7

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

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.
2. Relevant 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.
3. 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.

2. Nov 11, 2014

### 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.