The magnetic force on a particle of charge moving with a velocity through a region with a magnetic field is
If an electric field is also present in the region, then the net force due to the two fields is called the Lorentz force.
By definition of the cross product, the magnetic force must be perpendicular to both the velocity and the magnetic field. As a result of the perpendicularity with the velocity, the magnetic field cannot change the speed, but only the direction of the velocity. Hence it is always a centripetal force.
A particle that enters a uniform magnetic field, experiences a force of magnitude Since this force is perpendicular to the direction the object travels, it will undergo centripetal acceleration.
Find the radius of orbit for a particle of charge and mass moving with speed through a uniform magnetic field
Many devices leverage the circular motion of a charge particle moving through a uniform field. One such device is a mass spectrometer, which sorts the ions in a sample according to their mass to charge ratio.
Find the charge to mass ratio of a particle that travels with speed through a mass spectrometer set to along an orbit of radius
From the charge to mass ratio is
A rudimentary way to enrich uranium for use in nuclear energy or weaponry is to pass an ionized beam of vaporized uranium through a modified mass spectrometer known as a calutron. Assuming an electronmagnet that produces a magnetic field of magnitude and a voltage oven rated at a potential difference of are available, what is the radius of the path traveled by the uranium-235 being isolated? Assume the beam of vaporized nitrogen is ionized to a charge of
The Lorentz force is the force felt by a particle of charge moving with a velocity through a region with both an electric field and a magnetic field
The net force on a particle moving through a region with both electric and magnetic fields is just the vector sum of the fields.
Find the net force on a particle moving with velocity in a region with electric field and magnetic field
It is best to start with evaluating the cross product.
Now the Lorentz force is
A positron moves through a region in which the electric fields is uniform in the -direction and the magnetic field is uniform in the -direction. What is the direction of the terminal velocity of the positron?
- IndianFace, ., & Primefac, . Action of the Lorentz force bending the path of an electron in a magnetic field. Retrieved May 4, 2016, from https://commons.wikimedia.org/wiki/File:Action_of_the_Lorentz_force_bending_the_path_of_an_electron_in_a_magnetic_field.gif