Magnetic field changing speed of particle?

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SUMMARY

The discussion centers on the behavior of an electron in a magnetic field, specifically regarding its acceleration and speed. It is established that while the electron's velocity changes due to acceleration in the negative z direction, its speed remains constant because the force acting on it is always perpendicular to its direction of motion. Consequently, the kinetic energy (KE) of the electron does not increase, as indicated by the work-energy principle where the angle theta is π/2, resulting in zero work done.

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sparkle123
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From my textbook:
b6ce2abe.png

The example seems to contradict what is said above. The electron is accelerated in the negative z direction, so the velocity now has both an x-component and a z-component so the speed DOES change (magnitude larger)?
 
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Since the acceleration/Force is always perpendicular to the direction of motion of the electron only the velocity is changed not the speed. The electron does not gain any KE since W=Fdcos(theta) and theta in this case is pi/2.
 
got it thanks!
 

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