Calculating Magnetic Flux Needed for Ion Control

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SUMMARY

The discussion centers on calculating the magnetic flux density required for a magnet to control negative ions with a mass of 277 u, allowing them to pass through a narrow gap after being accelerated by a voltage of 3.0 kV. The relevant equations include QU = MV² / r and QVB = MV² / r, where r is the radius of the circular path (50 cm). Participants emphasize the need to determine the velocity of the ions post-acceleration to solve for the magnetic flux density, clarifying that the charge (Q) is not necessary for this calculation.

PREREQUISITES
  • Understanding of ion acceleration and kinetic energy concepts
  • Familiarity with the equations of motion in magnetic fields
  • Knowledge of mass-energy equivalence and voltage-energy relationships
  • Basic grasp of magnetic flux density and its implications in ion control
NEXT STEPS
  • Calculate the velocity of ions accelerated by a 3.0 kV voltage using energy concepts
  • Explore the relationship between magnetic flux density and ion trajectory
  • Study the implications of mass-to-charge ratios in magnetic fields
  • Investigate practical applications of magnetic control in ion beam technology
USEFUL FOR

Students in physics, engineers working with ion beam technologies, and researchers focusing on magnetic field applications in particle control.

tankarish
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Homework Statement


A magnet is used to control negative ions and only allow those with a specific mass to pass through a narrow gap opening . The magnet will bend the ion beam in a quarter circle of radius 50 cm .
In an experiment, a negative ion accelerated by a voltage of 3.0 kV.

Which magnetic flux density must the magnets have for these molecules with mass 277 u to follow the circular path through the magnet and get through the gap opening ?

Homework Equations


QU = MV ^ 2 * 1 / r , then mv ^ 2 * 1 / r = QVB

The Attempt at a Solution


Because we have volt , I think QU = MV ^ 2 * 1 / r , then mv ^ 2 * 1 / r = QVB
But we do not have Q, or v. Thus I do not know how I solve this .

Sorry for the English, but it seems the problem can't be solved?
 
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tankarish said:
QU = MV ^ 2 * 1 / r
I'm not sure what equation you are using here. What is U?

tankarish said:
But we do not have Q, or v.
You do not need Q to solve this question. You do, however, need v. This v would be the velocity of the negative ions after being accelerated by the voltage of 3kV, right before they enter the magnetic field. Can you find what is this v using the concept of energy?
Show us your working
 

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