Lagrangian of Particle Moving in Electromagnetic Field
Not what you're looking for?
An electromagnetic field is given by the potential:
phi = 0 and A = ay(z-hat) + bt(x-hat)
with a and b constant where 'x-hat?'z-hat?are unit vectors along the x and z directions respectively.
a. Write the Lagrangian for a particle of charge q moving in this field.
b. Identify any constants of the motion
c. Write the Hamiltonian
d. Find the value of the Hamiltonian as a function of time for an initial condition of the particle at rest at t=0
Purchase this Solution
Solution Summary
The solution examines Lagrangian of particles moving in an electromagnetic field. The constants of motion are determined. A Hamiltonian is given.
Solution Preview
Please see the attachment.
The potential due to a charge Q moving in an electromagnetic field described by the potentials is:
(1.1)
Where is the velocity vector:
(1.2)
In our case thus the potential energy here is:
(1.3)
The kinetic energy s simply:
(1.4)
So the general Lagrangian for this particle is:
(1.5)
In our specific case this turns out to ...
Purchase this Solution
Free BrainMass Quizzes
Basic Physics
This quiz will test your knowledge about basic Physics.
The Moon
Test your knowledge of moon phases and movement.
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
Variables in Science Experiments
How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.