Understanding the Formula r=mv/Bq in Grade 12 Physics

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SUMMARY

The formula r=mv/Bq is derived from the relationship between the magnetic force acting on a charged particle and the net force required for uniform circular motion. When a charged particle with charge q moves at velocity v perpendicular to a magnetic field B, the magnetic force F can be expressed as F=qvB. By equating this force to the centripetal force (F=ma), where a is the centripetal acceleration, the formula simplifies to r=mv/Bq. This derivation is essential for understanding the motion of charged particles in magnetic fields.

PREREQUISITES
  • Understanding of uniform circular motion principles
  • Knowledge of magnetic force equations, specifically F=qvB
  • Familiarity with centripetal acceleration and its relation to force
  • Basic algebra for rearranging equations
NEXT STEPS
  • Study the derivation of centripetal acceleration in detail
  • Explore the implications of the Lorentz force on charged particles
  • Learn about the applications of r=mv/Bq in particle physics
  • Investigate the role of magnetic fields in circular motion through simulations
USEFUL FOR

High school physics students, educators teaching electromagnetism, and anyone interested in the dynamics of charged particles in magnetic fields.

mayodt
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Where did the formula r=mv/Bq come from in my answerbook for my grade 12 physics? Thanks.
 
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mayodt said:
Where did the formula r=mv/Bq come from in my answerbook for my grade 12 physics? Thanks.

Do you know the equation for uniform circular motion, given a force F that always points toward the center of the circular motion?

Do you know the equation for the force F on a charged particle q when it is traveling at velocity v perpendicular to a magnetic field B?
 
berkeman said:
Do you know the equation for uniform circular motion, given a force F that always points toward the center of the circular motion?

Do you know the equation for the force F on a charged particle q when it is traveling at velocity v perpendicular to a magnetic field B?

F=qvBsin(theta) is the equation right? and, I probably have seen the first one, but can't remember that specific one.
 
mayodt said:
F=qvBsin(theta) is the equation right?

Correct, but what does it simplify to when the velocity and B-field are orthogonal (at right angles to each other)?


mayodt said:
and, I probably have seen the first one, but can't remember that specific one.

See Uniform Circular Motion at wikipedia, and remember that F=ma:

http://en.wikipedia.org/wiki/Uniform_circular_motion

.
 
berkeman said:
Correct, but what does it simplify to when the velocity and B-field are orthogonal (at right angles to each other)?




See Uniform Circular Motion at wikipedia, and remember that F=ma:

http://en.wikipedia.org/wiki/Uniform_circular_motion

.

Ohh okay I got it. Because the force of the magnetic field equals the net force (F=ma) so that means that qvb=ma and then since v=rw and a=vw it's qrwB=mvw, and then the w's cancel out and you rearrange. Thanks a lot :biggrin:
 
mayodt said:
Ohh okay I got it. Because the force of the magnetic field equals the net force (F=ma) so that means that qvb=ma and then since v=rw and a=vw it's qrwB=mvw, and then the w's cancel out and you rearrange. Thanks a lot :biggrin:

Good job! :biggrin:
 

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