CYCLOTRONIC MOTION
Orbital Radius ($r$)0.0 m
B-Field DirectionInto Page [X]
■ Classical Electrodynamics:
$\vec{F} = q(\vec{v} \times \vec{B})$
A moving charge in a uniform magnetic field experiences a force purely perpendicular to its instantaneous velocity. Because the force does no work ($W=\int F ds = 0$), it acts solely as a centripetal force resulting in uniform circular motion.
■ Cyclotron Radius:
$F_c = F_b$
$\frac{mv^2}{r} = qvB$
$r = \frac{mv}{qB}$
Notice that a heavier mass $m$ or faster velocity $v$ increases the turn radius, while a stronger $B$-field or greater $q$ tightens it.
$\vec{F} = q(\vec{v} \times \vec{B})$
A moving charge in a uniform magnetic field experiences a force purely perpendicular to its instantaneous velocity. Because the force does no work ($W=\int F ds = 0$), it acts solely as a centripetal force resulting in uniform circular motion.
■ Cyclotron Radius:
$F_c = F_b$
$\frac{mv^2}{r} = qvB$
$r = \frac{mv}{qB}$
Notice that a heavier mass $m$ or faster velocity $v$ increases the turn radius, while a stronger $B$-field or greater $q$ tightens it.