Revision as of 11:57, 25 August 2014

Charged Particle in uniform B-Field

Consider a charged particle moving the x-y plane in the presence of a uniform magnetic field with field lines in the z-dierection.

\vec{v} = v_x \hat i + v_y \hat j

\vec{B} = B \hat k

\vec{F} = q \vec{E}q\vec{v} \times \vec{B}

Note: the work done by a magnetic field is zero if the particle's kinetic energy (mass and velocity) don't change.; W = \Delta K.E.

No work is done on a charged particle force to move in a fixed circular orbit by a magnetic field (cyclotron)

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+=Charged Particle in uniform B-Field=
+Consider a charged particle moving the x-y plane in the presence of a uniform magnetic field with field lines in the z-dierection.
+:\vec{v} = v_x \hat i + v_y \hat j
+:\vec{B} = B \hat k
+;Lorentz Force
+:\vec{F} = q \vec{E}q\vec{v} \times \vec{B}
+;Note: the work done by a magnetic field is zero if the particle's kinetic energy (mass and velocity) don't change.
+:W = \Delta K.E.
+No work is done on a charged particle force to move in a fixed circular orbit by a magnetic field (cyclotron)
 [[Forest_Ugrad_ClassicalMechanics]]