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Physics - Magnetic effect?
I fully understand the relationships:
F = BIl, F = BIl.sin theta,
I = Q/t,
l or d = vt,
F = BQ/t.vt, F = BQv,
and:
F = ma,
a = v^2 / r,
F = mv^2 / r,
so:
mv^2 / r = BQv, mv^2 = BQvr, mv = BQr, v = BQr/m,
and finally, r = mv/BQ
but where does:
t = pi*r / v
come from, and how does that translate:
r = mv/BQ
to:
t = pi*m/BQ
i know that:
t = pi*r / v
stems from:
d = vt ==> t = d/v
but why is distance/length equivalent to pi*r
giving:
t = pi*r / v
yup i see how that works cos i already wrote that! but what i was looking for was, what you first mentioned, l = 2*pi*r, or one revolution. so thanks.
this revision page: (http://www.antonine-education.co.uk/Physics_A2/Mod...
didnt explain where it came from, and now i realise why pi*r is given (as opposed to 2*pi*r) - it's because the particle is accelerated in a spiral and we are calculating semi-circles (half a revolution).
but thanks.
1 Answer
- Sturm VogelLv 71 decade agoFavorite Answer
For your information, its 2πr / v. 2πr is the circumference, while v is obviously the velocity. That ratio is the amount of time needed to complete one revolution or one cycle. That comes from simple mathematics.
As for the radius equation, its simple. This came from the centripetal force equation, which is F = mv² / r. Force is also equivalent to F = qvB. That is the Lorentz force equation is magnetism. Therefore, the two equations are equal.
qvB = mv² / r
Rearranging that allows you to solve for r, which is...
r = mv² / qvB = mv / qB
