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

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The formula r=mv/Bq is derived from the relationship between magnetic force and centripetal force in uniform circular motion. When a charged particle moves perpendicular to a magnetic field, the magnetic force acting on it can be expressed as F=qvB. This force equals the centripetal force required for circular motion, F=ma, leading to the equation qvB=ma. By substituting the expressions for velocity and acceleration, the formula simplifies to r=mv/Bq. Understanding this derivation is crucial for grasping concepts in grade 12 physics.
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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