The picture shows the situation described

I have the above question and I have though about it every way and can't seem to find out. So what I have concluded (ignore the answers on the img) Is that the force is on the z axis because the cross product of the two would be the normal of the plane it lies on which is into or outof the screen.

Thus I am saying that first one is false because it is on the z axis, the finite amount I said true because it leaves the magnetic field when being pushed perpendicularly away. The next one because it IS normal to the velocity. Lastly the y-component is unchanged again because the force points the z direction not the y.

Any reasons to what I am thinking wrong any help would be appreciated.

  • $\begingroup$ Just because a force is always normal to the direction of travel doesn't mean that the object will necessarily travel in a circular orbit. $\endgroup$ – DumpsterDoofus Mar 14 '14 at 20:54
  • $\begingroup$ @DumpsterDoofus Okay that makes sense actually I was thinking perhaps the circular part would cause me issues I will try it out $\endgroup$ – capa_matrix Mar 14 '14 at 21:01
  • $\begingroup$ @DumpsterDoofus So according to the rest of my logic using false,true,false,true is still wrong so are there any other flaws I can't see $\endgroup$ – capa_matrix Mar 14 '14 at 21:03

You can simply decompose the velocity in its $v_x$ and $v_y$ components. The first one will remain unaffected (do a Galileo transformation, if you are not sure, and observe from a frame moving at $v_x(0)$ in the $x+$ direction).

The perpendicular component to the force will have a constant modulus, but its direction will change uniformly, so the particle will describe a helicoidal trajectory.

No one of the options is actually correct, but the last one is the closest (could just be bad wording). For the others:

  • The force is in the $YZ$ plane, never in $\vec x$
  • Magnetic forces cannot do work.
  • The particle has a constant $v_x$, so the trajectory cannot be circular.
  • $\begingroup$ Thankyou for the help you were right in that all of them were false. Thanks again. $\endgroup$ – capa_matrix Mar 14 '14 at 21:24

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