Velocity Filter/Selector: Only particles with a specific velocity pass through undeflected when forces balance.
Mass Spectrometry.
Electron Ballistics. [3, 11, 12, 13, 14]
Lorentz Force: Total force on a charged particle due to both fields (F=q(E+ v X B))
Force Balance: Electric force = Magnetic force (qEm= q(v X B))
The region in which uniform electric field is mutually perpendicular to uniform magnetic field is called as crossed configuration
Electron lenses: Used to focus and manipulate electron beams.
Electron beam focusing: Found in devices like electron microscopes and cathode ray tubes.
Velocity selectors: Principles are used to design instruments that select electrons of a specific velocity.
Similar to how light refracts at an interface between two media.
Difference: Bethe's Law uses velocities or potentials
X-component of velocity: Remains constant because the electric field is in the y-direction (v1x=v2x).
Y-component of velocity: Changes as the electron crosses the equipotential surface, gaining or losing kinetic energy.
Energy relation: The kinetic energy gained (qV) is related to the change in velocity (mv2/2)
Definition: An analogy to Snell's Law of Refraction for electrons passing between different electric potentials
Key idea: The normal component of the electron's velocity changes, while the tangential component remains constant.
Mass Spectrometry: Separates ions based on their mass-to-charge ratio by first selecting ions with a specific velocity.
Particle Accelerators: Selects particles with a specific energy to ensure a high-quality beam for experiments.
Plasma Physics: Used to study the properties of plasmas.
Electron Microscopes: Filters electrons to achieve a high-resolution image.
Molecular Beam Experiments: Selects molecules with a particular velocity for scattering and collision studies.
Condition of Undeflected travel: The electric and magnetic forces must cancel each other out FE =FB
Mathematical condition: qE=qVB.
Selected Velocity(v): Rearranging the equation gives the specific velocity of particle that pass through: v=E/B
Filtering process:
Particles with v = E/B travel in straight line
Particles with v>E/B experiences a stonger magnetic force and are deflected
Particles with v<E/B experiences a stronger electric force and are deflected
Electic Field(E): Gentrates by a pair of charged plates
Magnetic field (B): Gentrated by magnets oriented perpendicular to the electric Field and particle's path
Paticle Beam : An input stream of charged particles with varrying speed
Apertures: Slits or holes to define the incoming and outgoing beams
Electric Force (FE): FE = qE. the force is in the direction of of the E-field for a positive charge and opposite for a negative charge.
Magnetic Force(FB): FB = q(V x B) or Fb =qVB (When field was perpendicular).The force direction is given by right-hand rule
Lorentz Force: The total force on the particle is sum of the electric and magnetic forces: Ftotal = FB + FE
Balancing the electric force (FE) and magnectic force (FB) on the charged particle.
To allow only charged particle with a specific velocity to pass through undeflected
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