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Lesson 33 · The sideways push
A force that will not touch a stationary charge
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A force that will not touch a stationary charge

Electric fields push any charge, moving or not. Magnetic fields are pickier: they only notice charge that is MOVING, and they push it sideways. The magnitude is F=qvBsin⁡θF = qvB\sin\theta — read aloud F equals q v B sine theta. FF is the magnetic force in newtons; qq is the charge magnitude in coulombs; vv is its speed in metres per second; BB is the magnetic flux density in teslas (T); and θ\theta (theta) is the angle between the velocity and the field lines. Whichever one the question leaves blank is the one you solve for.

The tesla is a big unit and worth calibrating against: Earth's field is about 50 μT50\ \mu\mathrm{T}, a fridge magnet about 5 mT5\ \mathrm{mT}, a hospital MRI bore 1.5 to 3 T. If your answer says the lab bench is running at 40 T, something upstream is lying.

Everything interesting lives in that sin⁡θ\sin\theta. Fly ALONG the field lines and θ=0\theta = 0, sin⁡0=0\sin 0 = 0, and the force is exactly nothing. Sit still and v=0v = 0, and again nothing. Cut straight ACROSS at 90∘90^\circ and sin⁡90∘=1\sin 90^\circ = 1 — maximum push. Reach for cos⁡\cos instead and you have claimed the force peaks where it actually vanishes. And one more fact, free now and load-bearing at the boss: the force is perpendicular to the motion, so it does no work. It never speeds a charge up. It only turns it.

qvFB

F=qvBsin⁡θF = q v B \sin\theta

  • FF= Magnetic force (force)
  • qq= Charge (electric charge)
  • vv= Speed (speed)
  • BB= Magnetic flux density (magnetic flux density)
  • θ\theta= Angle between v and B (angle)
Magnetic Force on a Moving Charge solver →