Consider a magnetic field B-ky e3 for x>0 and B=0 for x<0, where k>0 is a constant. A beam of particles of charge q, mass m, moving in the x-y plane is incident from the left (x<0), traveling at constant velocity v=vo e₁ in the x direction along the line y-yo.

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Chapter11: Magnetic Forces And Fields
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7. Consider a magnetic field B=ky ez for x>0 and B=0 for x<0, where k>0 is a constant.
A beam of particles of charge q, mass m, moving in the x-y plane is incident from the
left (x<0), traveling at constant velocity v=vo ej in the x direction along the line y=yo.
Neglecting any change in the x-component of velocity (that is, assuming that vi
remains equal to vo), determine the orbits in the magnetic field for both q>0 and q<0.
NOTE: the above field is a quadrupole field used to focus or defocus charged
particles.
Transcribed Image Text:7. Consider a magnetic field B=ky ez for x>0 and B=0 for x<0, where k>0 is a constant. A beam of particles of charge q, mass m, moving in the x-y plane is incident from the left (x<0), traveling at constant velocity v=vo ej in the x direction along the line y=yo. Neglecting any change in the x-component of velocity (that is, assuming that vi remains equal to vo), determine the orbits in the magnetic field for both q>0 and q<0. NOTE: the above field is a quadrupole field used to focus or defocus charged particles.
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