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https://texercises.raemilab.ch/exercise/trajectory-in-a-combined-electric-and-magnetic-field/
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Exercise:
A uniform electric and a uniform magnetic field po in the same direction. Describe the path of a charged particle initialle moving perpicularly to the fields.

Solution:
The electric field causes a force along the direction of the electric field that increases the kinetic energy of the charged particle i.e. the component of the velocity vector in this direction increases over time. The force caused by the magnetic field is not affected by the velocity component parallel to the field. It is therefore constant in magnitude and causes a circular motion in the projection to a plane perpicular to the field. The combined trajectory is a helical path with an increasing distance between neighbouring turns. It looks like a helical spring which is stretched more towards one side than the other. The figure below shows the result of a Python simulation for the motion of an electron entering an electric field and a magnetic field poing in the negative x-direction. The python file is attached to the solution and can be used to investigate other orientations of the fields and the initial velocity. center includegraphicswidthtextwidth#image_path:electron-in-parallel-and-b-field# center
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Exercise:
A uniform electric and a uniform magnetic field po in the same direction. Describe the path of a charged particle initialle moving perpicularly to the fields.

Solution:
The electric field causes a force along the direction of the electric field that increases the kinetic energy of the charged particle i.e. the component of the velocity vector in this direction increases over time. The force caused by the magnetic field is not affected by the velocity component parallel to the field. It is therefore constant in magnitude and causes a circular motion in the projection to a plane perpicular to the field. The combined trajectory is a helical path with an increasing distance between neighbouring turns. It looks like a helical spring which is stretched more towards one side than the other. The figure below shows the result of a Python simulation for the motion of an electron entering an electric field and a magnetic field poing in the negative x-direction. The python file is attached to the solution and can be used to investigate other orientations of the fields and the initial velocity. center includegraphicswidthtextwidth#image_path:electron-in-parallel-and-b-field# center
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Branches
Magnetism
Tags
electric field, electron, magnetic field, trajectory
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
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Descriptive / Quality
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