Introductory Physics Volume Two

86 Magnetic Fields 4.5
(a) Show that if v = E/B that the particles will go straight through
the region without deflection.
(b) Show that if v > E/B and q > 0 then the particles will be deflected
in the negative y direction.
(c) Show that if v > E/B and q < 0 then the particles will be deflected
in the positive y direction.
(d) Show that if v < E/B and q > 0 then the particles will be deflected
in the positive y direction.
A device setup with crossed magnetic and electric fields as in the
previous problem is called a velocity selector. Since it sorts out the
particles based on their speeds, if you select out just the ones that
go straight ahead, you have selected particles with a particular speed
v = E/B. By adjusting the field strengths you can choose what velocity
you would like to select.
§ 4.5 Hall Effect
Let us look with more detail at the flow of current in a wire that
is in a magnetic field. Suppose that we have a rectangular conductor
with a current I running through it.
w
h
If we consider the charges in the wire we see that there will be a
magnetic force on the particles that will tend to deflect them to one
face of the conductor.
I
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I
But this force will be acting on all the free charges, so they will all shift
upward as they move through the conductor. Keeping in mind that
the positive charge in the conductor does not move, we see that this
shift of the (negative) free charges will build up a net negative charge
on one face of the conductor and net positive charge on the opposing
face.
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