Radius of path of electron in a magnetic field

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SUMMARY

The radius of the circular path of an electron in a magnetic field of 50 Oersted with a velocity of 8.8 x 10^6 cm/sec is calculated using the formula r = (mVc)/(Be). Initially, the user incorrectly applied the formula r = (mV)/(Be), resulting in an unreasonably small radius of 3.3 x 10^(-13) cm. By correcting the formula to include the speed of light (c), the user arrived at a more accurate result. This discussion highlights the importance of using the correct Lorentz force equation in the C.G.S system.

PREREQUISITES
  • Understanding of C.G.S (Centimeter-Gram-Second) units
  • Familiarity with the Lorentz force equation
  • Knowledge of electron charge and mass values
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the derivation of the Lorentz force equation in various unit systems
  • Learn about the implications of magnetic fields on charged particles
  • Explore the concept of cyclotron motion and its applications
  • Investigate the differences between C.G.S and SI units in electromagnetism
USEFUL FOR

Students of physics, educators teaching electromagnetism, and researchers working with charged particle dynamics in magnetic fields.

Amith2006
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# Electrons are moving in a uniform magnetic field of 50 Oersted having a velocity of 8.8 x 10^6 cm/sec. What is the radius of the circular path they follow?
I solved it in the following way:
In C.G.S system 1 Gauss = 1 Oersted (In vacuum)
So, B = 50 Gauss
V = 8.8 x 10^6 cm/sec
Let e be the charge of the electron, r be radius of its circular path and m be its mass.
e = 1.6 x 10^(-19) Coulomb = 4.8 x 10^(-10) Stat Coulomb
m = 9.1 x 10^(-28) grams
In a perpendicular magnetic field,
BeV = {m(V^2)}/r
r = (mV)/(Be)
Solving I get,
r = 3.3 x 10^(-13) cm
I think somewhere I have gone wrong as the radius is too small. Please help.
 
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In cgs units the formula for the Lorentz force is (qv/c) x B. The final formula should read r = (mVc/Be). This gaves a much more reasonable answer.
 
I have learned the expression for Lorentz force in C.G.S system.Thanks.
 

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