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A charge in a magnetic field

A charged particle moving perpendicular to a uniform magnetic field feels a force perpendicular to its velocity. The force changes the direction but not the speed, so the particle moves in a circle. The radius becomes larger if the mass or the speed increases, and smaller if the charge or the field increases. A neutral particle feels no magnetic force. If the charge moves parallel to the field, the force is zero too.

r = \frac{mv}{qB}

radius when the velocity is perpendicular to the field

Symbols

$m$	mass	kg
$v$	speed	m/s
$q$	charge	C
$B$	flux density	T

Example

A particle has mass 0.004 kg, charge 0.02 C and speed 10 m/s in a field of 0.5 T.

$r = \dfrac{0.004 \cdot 10}{0.02 \cdot 0.5} = 4$ m.

The magnetic force does no work. The kinetic energy is therefore constant along the path.

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Part of Physics 2: Electromagnetism.