Particle in a static E field Consider a charge particle q interacting with a E field E Ex Particle s initial conditions p t 0 p0y The Lorentz force is integrate So that total energy a time t is P Piot PHYS 571 Fall 2007 Particle in a static E field The velocity is then Integrate Similarly for y axis we have Integrate P Piot PHYS 571 Fall 2007 Particle in a static E field Explicit t as a function of y And insert in x t Note the NR limit P Piot PHYS 571 Fall 2007 Particle in a static E field P Piot PHYS 571 Fall 2007 Particle in a static B field Consider a charge particle q interacting with a B field B Ez Particle s initial conditions p t 0 p0y The Lorentz force is From We get the 3 equations P Piot PHYS 571 Fall 2007 Particle in a static B field These are a system of 3 coupled ODEs of the form with We can cast the transverse equations into one equation Whose solution is so finally P Piot PHYS 571 Fall 2007 Particle in a static B field This is the equation of an helix with axis along z and radius R R is the gyro radius is the gyro frequency In SI units P Piot PHYS 571 Fall 2007
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