i need help understanding the direction of the electric force
for the folloeing image
using the right hand rule 1 i was able to determine the direction of the magnetic force. the direction of the magnetic force is down because, it is electrons in motion, and electrons are negative, that is why it is down but i dont understand why the electric force is up. how do i fihure that out?
The magnetic flux linked by the circuit is simply the product of
the perpendicular magnetic field-strength, , and the area of the circuit,
, where
determines the position of the
sliding rod. Thus,
![]() |
(202) |
Now, the rod moves a distance in a time interval
, so in the same time interval
the magnetic flux linking the circuit increases by
![]() |
(203) |
It follows, from Faraday's law, that the magnitude of the emf
generated around the circuit is
given by
![]() |
(204) |
Thus, the emf generated in the circuit by the moving rod is
simply the product of the magnetic field-strength, the length of
the rod, and the velocity of the rod. If the magnetic field is not
perpendicular to the circuit, but instead subtends an angle
with respect to the normal
direction to the plane of the circuit, then it is easily
demonstrated that the motional emfgenerated in the circuit
by the moving rod is
![]() |
(205) |
where is the component of the
magnetic field which is perpendicular to the plane of the
circuit.
Since the magnetic flux linking the circuit increases
in time, the emf acts in the negative direction
(i.e., in the opposite sense to the fingers of a
right-hand, if the thumb points along the direction of the magnetic
field). The emf, , therefore, acts in the
anti-clockwise direction in the figure. If
is the total resistance of the
circuit, then this emf drives an anti-clockwise electric current of
magnitude
around the circuit.
But, where does the emf come from? Let us again remind ourselves
what an emf is. When we say that an emf acts around the circuit in the
anti-clockwise direction, what we really mean is that a charge
which circulates once around the
circuit in the anti-clockwise direction acquires the energy
. The only way in which the
charge can acquire this energy is if something does work
on it as it circulates. Let us assume that the charge circulates
very slowly. The magnetic field exerts a negligibly small
force on the charge when it is traversing the non-moving part of
the circuit (since the charge is moving very slowly). However, when
the charge is traversing the moving rod it experiences an
upward (in the figure) magnetic force of magnitude
(assuming that
). The net work done on the
charge by this force as it traverses the rod is
![]() |
(206) |
since . Thus, it would appear that the
motional emf generated around the circuit can be accounted for in
terms of the magnetic force exerted on charges traversing the
moving rod.
But, if we think carefully, we can see that there is something
seriously wrong with the above explanation. We seem to be saying
that the charge acquires the energy from themagnetic field
as it moves around the circuit once in the anti-clockwise
direction. But, this is impossible, because a magnetic field
cannot do work on an electric charge.
Let us look at the problem from the point of view of a charge
traversing the moving rod. In
the frame of reference of the rod, the charge only moves very
slowly, so the magnetic force on it is negligible. In fact, only an
electric field can exert a significant force on a slowly moving
charge. In order to account for the motional emf generated around
the circuit, we need the charge to experience an upward force of
magnitude
. The only way in which this is
possible is if the charge sees an upward pointing electric
field of magnitude
![]() |
(207) |
In other words, although there is no electric field in the
laboratory frame, there is an electric field in the frame of
reference of the moving rod, and it is this field which does the
necessary amount of work on charges moving around the circuit to
account for the existence of the motional emf,
More generally, if a conductor moves in the laboratory frame
with velocity in the presence of a magnetic
field
then a charge
inside the conductor experiences
a magnetic force
. In the frame of the conductor,
in which the charge is essentially stationary, the same force takes
the form of an electric force
, where
is the electric field in the
frame of reference of the conductor. Thus, if a conductor moves
with velocity
through a magnetic field
then the electric field
which appears in the rest frame
of the conductor is given by
![]() |
(208) |
This electric field is the ultimate origin of the motional emfs which are generated whenever circuits move with respect to magnetic fields.
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