How Does a Positron's Kinetic Energy Change with Magnetic Field Strength?

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SUMMARY

The kinetic energy (KE) of a positron moving in a circular path is directly related to the strength of the magnetic field (B) when maintaining a constant radius (R). The relationship is established through the equation 2RqvB = KE, indicating that KE is proportional to B squared (KE ∝ B²). This quadratic relationship results in a graph that is a quadratic function centered at zero. The discussion clarifies that while velocity (v) depends on KE, the proportionality of KE to B² is definitive.

PREREQUISITES
  • Understanding of magnetic fields and their effects on charged particles.
  • Familiarity with the equation of motion for circular motion in a magnetic field (qvB = mv²/R).
  • Knowledge of kinetic energy calculations (KE = 1/2MV²).
  • Basic algebra skills for manipulating equations and understanding proportional relationships.
NEXT STEPS
  • Study the derivation of the Lorentz force and its implications for charged particles in magnetic fields.
  • Explore the concept of circular motion in magnetic fields and its applications in particle physics.
  • Investigate the graphical representation of quadratic functions and their properties.
  • Learn about the relationship between kinetic energy and momentum in the context of electromagnetic fields.
USEFUL FOR

Students in physics, particularly those studying electromagnetism, as well as educators and anyone interested in the dynamics of charged particles in magnetic fields.

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Homework Statement


A positron moves in a circular path of radius R due to a uniform magnetic field of strength B applied perpendicular to the plane of the circle. If B is varied, which of the following best represents a graph of the kinetic energy of the positron as a function of B so that the positron maintains the same radius R.

Homework Equations


qvB=mv^2/R

The Attempt at a Solution


KE = 1/2MV^2

Rearranging first equation, RqvB =mv^2, then multiply each side by 2

2RqvB = KE

Here i thought that KE is proportional to B, but v remains a variable that depends on KE. How do create a relationship between B and KE?
 
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Try using qvB=mv2/R to get an expression for v.
 
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Wow. I don't know how I messed that up. Graph is quadratic. Thanks for your help!
 
Good work.
 
2RqvB = KE

You could also note that v is proportional to KE^(1/2), and then since you don't need to worry about constants such as 1/2m you can just say that 2q KE^1/2 B is proportional to KE, and by dividing KE ^1/2 on both sides you get 2qB is proportional to KE^1/2.
so KE is proportional to B^2 and you get the answer that it is a quadratic formula centered at 0.
 

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