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Electricity & Magnetism
Electricity & Magnetism

Cyclotron Radius

r=mvqBr = \frac{mv}{qB}

Radius of circular motion of charged particle in magnetic field.

Variables

r
Radius
Radius of circular path
m
m
Mass
Particle mass
kg
v
Velocity
Particle speed
m/s
q
Charge
Particle charge
C
B
Magnetic field
Field strength
T

Derivation

From qvB = mv²/r (Lorentz force = centripetal force), r = mv/(qB).

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Common questions

What is the Cyclotron Radius formula?

Cyclotron Radius is written r = mv/qB. Radius of circular motion of charged particle in magnetic field. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in r = mv/qB?

In SI units, r is radius, measured in m; m is mass, measured in kg; v is velocity, measured in m/s; q is charge, measured in A·s; B is magnetic field, measured in kg/(A·s²).

How is the Cyclotron Radius formula derived?

From qvB = mv²/r (Lorentz force = centripetal force), r = mv/(qB). The result is r = mv/qB.