Electromagnetism

Breif history of the concept of the field

The Electric Field

The Magnetic Field

Faraday's Law

Movement of charged
particles in an electromagnetic
field

Measuring the charge/mass
ratio

Measuring the fundamental 
unit of charge

The Mass Spectrometer

The Cyclotron

Dielectric Materials

Paramagnetism

Ferromagnetism

Kinematics

Circular Motion

Linear Acceleration

Semicircular Region

Activities

Introduction

The Bainbridge spectrometer is a device that separates ions that have the same velocity. After crossing the slits, the ions pass through a velocity selector, a region in which there exists a crossed electric and magnetic field. The ions that pass through the velocity selector without being accelerated to the side enter a semicircular region where the magnetic field forces the ions to follow a circular trajectory. The radius of the orbit is proportional to the mass, which is why ions of different mass hit in different places on the screen (which also functions as a graduated scale).

The objective of this program consists of counting the number of isotopes of an element and finding their masses in atomic mass units. The key to doing so is based on knowing that the orbital diameter depends on the exact magnitudes of the electric and magnetic fields, and by measuring the orbital diameter using the graduated scale.

We will calculate the mass (in atomic mass units) of each isotope and verify with the program if we have guessed right or not in the calculation. .

Velocity Selection

The selection of speeds occurs in a region in which an electric field and a magnetic field
exist perpendicular to each other and, likewise, perpendicular to the direction of the velocity vector of the ion. In this region the ions of a certain speed are specificially selected.

The electric field exerts a force in the direction of the field whose magnitude is

The magnetic field exerts a force whose direction is determined by the
vector cross product  , and whose magnitude is

The ion moves in a straight line only if both forces are equal and opposite.   Since the magnetic field force depends on the speed of the ion, those ions not having the proper speed will be accelerated to one side.  Therefore, the only ions that move in a straight line through the velocity selector are those with a speed given by the quotient between the electrical magnetic field and field strength,

Semicircular Region

Next, the ions enter the semicircular region, where the magnetic field causes
that they describe semicircular trajectories until they reach the superior board in
which they are deposited.

In the semicircular region the ion experiences a force due to the magnetic field,
whose direction and felt it comes given by the vectorial product , with the magnitude .

Applying to the equation of the dynamics of the circular movement uniform, we
found the radius of the circular trajectory

Activities (in Spanish)