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FORCE ON A CHARGED MOVING PARTICLE IN A MAGNETIC FIELD

         Remember in motors how a current in a magnetic field caused a force on a wire? Movement of a wire in a magnetic field causes a force on the electrons too! This is because in the wire, electrons are being moved as the wire moves, the effect being movement of electrons, which constitutes a current flowing. Firing an electron, or any other charged particle, into a field, has exactly the same effect: a force is exerted on the particle, causing it to change direction.

         You should already be ahead: if a current is flowing in a magnetic field the force will depend on the direction of the magnetic field according to Fleming's Left Hand Rule. But remember; conventional current flows in the opposite direction to the electrons due to convention!

         Consider a charged particle q travelling at constant speed v at right angles to a magnetic field of flux density B.

         Read that again. It's important. OK.

         So the moving charge constitutes a current, q/t.

         If we substitute our friend Bill in here, we get:
F = BIl = Bq l/t

         If the particle travels distance l in time t, v=l/t, so

      F = Bqv

         So what? I'll tell you what. The force makes the particle accelerate and therefore change direction... So, the direction of the force changes, so the direction of the force changes, so the direction of acceleration changes again... You get the picture.

         Sound familiar? What if I tell you that the force is of constant magnitude and always at right angles to the velocity? Oh no! It's circular motion all over again! So:

         F = mv2

r

         If we have two equations for the force so we can combine them- what fun!
F = B q v = m v2

r

         One you often get asked is the radius of the circle as a charged particle moves through a magnetic field. Easy! Simply rearrange:

      r = mv2
      Bq

(If that doesn't cheer you up then nothing ever will).

 

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