The discussion revolves around a problem involving a singly charged lithium ion accelerated by an electric field and subsequently moving through a magnetic field, resulting in circular motion. The participants explore how to determine the radius of the ion's circular path, which is stated to be 7.06 cm.
The discussion is active, with participants providing insights into the forces acting on the ion and how they relate to its motion. Some guidance has been offered regarding the equations involved, but there is no explicit consensus on the proofs or interpretations being explored.
Participants are navigating through the implications of the electric and magnetic fields on the ion's trajectory, questioning assumptions about force relationships and the definitions of terms used in the context of the problem.
I believe one wishes to show that Force, F = [itex]\Del V[/itex], where [itex]V[/itex] is the potential energy function.silvan said:How do you prove the following?
force=-(del velocity)
As masudr indicated, the Li+ ion is accelerated across the potential, where F = qE, and the energy gained is just F*d. Then in the magnetic field, the particle of velocity v is subjected to a force q(v x B) where v x B is the cross product of the velocity and magnetic field. The resulting Lorentz force equals the centripetal force.astronomophosis said:A singly charged lithium ion is accelerated by an electric field E=10i V/m applied between two plates ten centimeters apart. After passing through a small hole in the negative plate, the ion enters a region of space where there is a magnetic field B=5j mT. The ion moves in a circular path. What is the radius of this circle? The answer to this problem is 7.06 cm. How is this found?