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Motion in a constant uniform electric field

Motion in a constant uniform electric field. Section 20. This derivation is relativisitically correct. Choose coordinates so that X is parallel to E . Choose inertial reference frame so that there is no motion of charge e along Z. Then, the motion of e is confined to the XY plane.

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Motion in a constant uniform electric field

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  1. Motion in a constant uniform electric field Section 20

  2. This derivation is relativisitically correct • Choose coordinates so that X is parallel to E. • Choose inertial reference frame so that there is no motion of charge e along Z.

  3. Then, the motion of e is confined to the XY plane. Y E e X

  4. To obtain the trajectory… 1. Obtain equation of motion in terms of relativistic momentum.

  5. Integrate to obtain momentum vs. time.

  6. Obtain the kinetic energy ekin as function of time

  7. Use equations of relativistic dynamics to obtain differential equation for velocity.

  8. Integrate to obtain coordinates as function of time

  9. Eliminate tto obtain x vs. y: The trajectory.

  10. v<<c

  11. What is the relativistically correct trajectory of an electron in a constant uniform electric field? • A hyperbola • A catenary • A parabola 1 2 3

  12. Trajectory is a Catenary

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