Vedatom Physics
Electromagnetism / Magnetic Field & Force
◈ Sims ▤ Full book
Magnetic force — the rules
Lorentz force F = qv × B is always ⟂ to v, so it does no work — it bends the path but never changes the speed.
Directions. = field/current out of the page, = into the page. Point fingers along v, curl toward B: the thumb gives v × B (flip it for a negative charge).
Circular motion. r = mv/(qB), period T = 2πm/(qB) — the period is independent of speed. That is the cyclotron principle.
Wire & loop. Force on a current F = I L × B; a loop feels no net force in a uniform field but a torque τ = m × B, with moment m = NIA.
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EM Lab · all topics
§02

The Lorentz force — a sideways push on a moving charge

The magnitude is F = qvB sinθ, θ being the angle between v and B. Send the field across the page (→) and the force pops straight out of it (⊙ / ⊗), scaling with sin θ. Send the field through the page (⊗ / ⊙) and the force lies in the plane, square to v — the very push that will curl the charge into a circle overleaf. Hit play to launch the charge and flip the field to feel the difference.

B → B {{ lFieldGlyph }} v F {{ lqSign }} F {{ lFdir }}
direction of v (θ from B / from horizontal){{ lThlab }}°
charge |q| (units of e){{ lQlab }} e
speed v (×10⁶ m/s){{ lVlab }}
field B (T){{ lBlab }}
F = |q| v B sin θ
force F
{{ lF }}
direction
{{ lFdir }}
sin θ factor
{{ lSin }}
work done
0 J
{{ lHead }} {{ lBody }}
§03

A charge in a magnetic field goes in circles

Fire a charge straight across a uniform field and that perpendicular force becomes a perfect centripetal pull: the charge loops at radius r = mv/(qB). The astonishing part is the clock — the period T = 2πm/(qB) has no v in it at all. Speed the charge up and its circle grows in exact step, so every lap takes the same time. Flip the charge or the field and watch the sense of rotation reverse.

FIELD {{ oFieldLabel }}
{{ oSignChar }} r = {{ oRlab }}
speed v{{ oVlab }}
field |B|{{ oBlab }} T
mass number A{{ oA }}
charge number Z{{ oZ }} e
r =m vq B T =2π mq B
radius r
{{ oRlab }}
period T
{{ oTlab }}
frequency f
{{ oFlab }}
kinetic energy
{{ oKlab }}
now spinning {{ oSense }}. Speed up and r grows, but T holds — the cyclotron's secret.