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Motional Emf
Consider the bar in the figure below. It has length l and
moves at speed v to the right in magnetic
field B, which is directed
into the page.
The field exerts a magnetic force on the free electrons
in the bar. That force is 
: using the right-hand
rule, you will find that the 
vector is directed upward
along the bar, but since electrons are negatively charged, the magnetic
force acting upon them is directed downward. As a result, electrons
flow to the bottom of the bar, and the bottom becomes negatively
charged while the top becomes positively charged.
: using the right-hand
rule, you will find that the vector is directed upward
along the bar, but since electrons are negatively charged, the magnetic
force acting upon them is directed downward. As a result, electrons
flow to the bottom of the bar, and the bottom becomes negatively
charged while the top becomes positively charged.The separation of charge in the rod creates an electric
field within the bar in the downward direction, since the top of
the bar is positively charged and the bottom of the bar is negatively
charged. The force from the electric field, 
, pulls negative charges upward while the
force from the magnetic field pulls negative charges downward. Initially, the
magnetic field is much stronger than the electric field, but as
more electrons are drawn to the bottom of the bar, the electric
field becomes increasingly stronger. When the two fields are of
equal strength, the forces balance one another out, halting the
flow of electrons in the bar. This takes place when:
, pulls negative charges upward while the
force from the magnetic field pulls negative charges downward. Initially, the
magnetic field is much stronger than the electric field, but as
more electrons are drawn to the bottom of the bar, the electric
field becomes increasingly stronger. When the two fields are of
equal strength, the forces balance one another out, halting the
flow of electrons in the bar. This takes place when:
Induced Current and Motional Emf
The electric field in the metal bar causes a potential
difference of V = El = vBl.
If the bar slides along metal rails, as in the figure below, a closed
circuit is set up with current flowing in the counterclockwise direction,
up the bar and then around the metal rail back to the bottom of
the bar. This is called an induced current.
The moving bar is a source of an electromotive force,
called motional emf, since the emf is generated by
the motion of the bar.
The force is defined as:
The magnitude of the induced emf can be increased by increasing
the strength of the magnetic field, moving the bar faster, or using
a longer bar.
Example
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Now that we’ve defined motional emf, solving this problem
is simply a matter of plugging numbers into the appropriate equation:
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