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

In summary, a charged particle with a mass of 1.673*10^-27 kg is placed in a region with an electric field of 10 kV/m in the x direction and a magnetic field of 1T in the y direction. The goal is to calculate the kinetic energy of the particle if it moves without being deflected. Using the equations F=Q(E+u x B) and KE=1/2 mu^2, and techniques from multivariable calculus, differential equations, and linear algebra, the velocity can be found and then used to calculate the kinetic energy. The solution also involves using the identity u x B = the magnitudes of u*b sinθ. It is important to note that the charge
  • #1
Vagabond7
50
11

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.
 
Physics news on Phys.org
  • #2
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.
 

1. How is the Lorentz Force Equation used to find the kinetic energy of a particle?

The Lorentz Force Equation is used to calculate the force exerted on a charged particle in an electromagnetic field. This force can then be used to determine the change in kinetic energy of the particle over a certain distance.

2. What is the formula for the Lorentz Force Equation?

The Lorentz Force Equation is F = q(E + v x B), where F is the force, q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

3. How does the electric and magnetic field affect the kinetic energy of a particle?

The electric and magnetic fields can change the direction and magnitude of the velocity of a charged particle, resulting in a change in its kinetic energy. The Lorentz Force Equation takes into account the effects of both fields on the particle's movement.

4. Can the Lorentz Force Equation be used for all types of particles?

Yes, the Lorentz Force Equation can be used for any charged particle, regardless of its mass or charge. This includes electrons, protons, and other subatomic particles.

5. How is the Lorentz Force Equation used in real-world applications?

The Lorentz Force Equation is used in a variety of real-world applications, such as particle accelerators, mass spectrometers, and electric motors. It is also used in the study of cosmic rays and the behavior of particles in space.

Similar threads

Replies
7
Views
962
  • Advanced Physics Homework Help
Replies
1
Views
842
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
21
Views
1K
  • Advanced Physics Homework Help
Replies
11
Views
972
  • Advanced Physics Homework Help
Replies
13
Views
4K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
9
Views
1K
Back
Top