Electron velocity and unit vector notation

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SUMMARY

An electron with an initial velocity of 0 m/s in the x-direction, 17.2 km/s in the y-direction, and 20.7 km/s in the z-direction experiences a constant acceleration of 1.95 x 1012 m/s2 in the positive x-direction. The magnetic field is 378 µT in the positive x-direction. To find the electric field components (Ex, Ey, Ez), the equation E = (ma/q) + B x V is applied, where F = q(E + v x B) = ma is the fundamental relationship governing the forces acting on the electron.

PREREQUISITES
  • Understanding of classical mechanics, specifically Newton's second law.
  • Familiarity with electric and magnetic fields and their interactions.
  • Knowledge of vector notation and operations, including cross products.
  • Basic understanding of charge, mass, and their units in physics.
NEXT STEPS
  • Study the concept of the Lorentz force and its applications in electromagnetism.
  • Learn about the mathematical properties of cross products in vector calculus.
  • Explore the derivation and implications of the equation F = q(E + v x B).
  • Investigate the role of electric fields in particle motion within magnetic fields.
USEFUL FOR

Physics students, educators, and anyone interested in understanding the dynamics of charged particles in electromagnetic fields.

4eleven
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Homework Statement


An electron has an initial velocity with an x component of zero, a y component of 17.2 km/s, a z component 20.7 km/s, and a constant acceleration of 1.95 x 1012 m/s2 in the positive x direction in a region in which uniform electric and magnetic fields are present. If the magnetic field has a magnitude of 378 µT and is in the positive x direction, find the (a)x, (b)y, and (c)z components of the electric field. Give your answers in V/m


Homework Equations


F = q(E + v x B) = ma
E = (ma/q) + B x V


The Attempt at a Solution


E = [(9.11E-31 kg*1.95E12 m/s) / -1.60E-19 C] + (378 uT)i x [(17.2 km/s)j + (20.7 km/s)k]

this may seem silly, but I can't remember how to solve for each x, y, and z component now...
 
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