Question regarding radius of circular paths (chapter the nucleus)

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SUMMARY

The discussion focuses on calculating the radius of circular paths taken by electrons in a magnetic field after they gain kinetic energy (K.E) from an electric potential. The kinetic energy is derived from the equation eV = 1/2 mv², where e is the charge of the electron, V is the potential, m is the mass of the electron, and v is the velocity. The centripetal force required for the circular motion is provided by the magnetic force, expressed as F = -e(V x B) = m(v²/R), allowing for the calculation of the radius (R) of the electron beam.

PREREQUISITES
  • Understanding of kinetic energy and its relation to electric potential (eV = 1/2 mv²).
  • Knowledge of the behavior of charged particles in magnetic fields.
  • Familiarity with the concepts of centripetal force and magnetic force.
  • Basic understanding of vector cross products in physics (V x B).
NEXT STEPS
  • Study the derivation of kinetic energy from electric potential in detail.
  • Learn about the motion of charged particles in magnetic fields, focusing on Lorentz force.
  • Explore the mathematical relationship between centripetal force and magnetic force.
  • Investigate practical applications of electron beams in devices like cyclotrons and mass spectrometers.
USEFUL FOR

Physics students, educators, and professionals in fields related to electromagnetism and particle physics will benefit from this discussion, particularly those interested in the dynamics of charged particles in magnetic fields.

Sanosuke Sagara
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I have my doubt,solution and question in the attachment that followed.Thanks for anybody that spend some time on this question.
 

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OK the problem with your solution is that You have made it a bit too complicated.
First of all ,
After accelerating through a potential , the electrons gain certain amount of K.E , which can be calculate din the following way:

[itex]eV= \frac{1}{2}mv^2[/itex]

From The KE , calculate velocity gained by the electron beam.

Now if you have studied how charged particles behave in magnetic fields, you should know that electrons when enter prependicular to a magnetic field, start moving in a circle.

Force due to a Magnetic field on an electron provides the centripedal force necessary for moving in circle. therefore,

[itex] F= -e(VxB) = m \frac{v^2}{R}[/itex]

From here calculate the radius of the beam...easy ..isnt it?
 
Yes,Dr Brain.Thanks for your help and I really appreciate it.Thanks again for your explanation in detail.
 

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