Magnetic field changing speed of particle?

AI Thread Summary
The discussion revolves around the effects of magnetic fields on an electron's motion. It highlights that while the electron's velocity changes due to acceleration in the negative z direction, its speed remains constant because the force is always perpendicular to its motion. Consequently, the electron does not gain kinetic energy, as the work done is zero when the angle is 90 degrees. This clarification addresses a common misconception about the relationship between velocity and speed in magnetic fields. Understanding these principles is crucial for grasping the dynamics of charged particles in magnetic fields.
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!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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