The Faraday's law of induction,
elaborated by Michael Faraday in 1832, states that the induced
current in a closed circuit involving a magnetic field is proportional to the
number of flow lines running through the area involved the circuit per unit of
time.
Franz Ernst Neumann, in 1845, wrote the law
mathematically:
∆ F = I X B ∆s
Where the magnetic flux, defined as:
φB = ∫ E ∙ dS
The surface S is any surface whose edge is
the circuit that is suffering induction. Using the definition of FEM and making
infinitesimal have:
∫ E dl = - dφ/dt.
By definition, the symbol E is the induced
electrical field, dl is a circuit element and dφ/dt is the variation
of magnetic flux in time. Heinrich Lenz has added the negative sign
in equation 1833 because it was found that the induced current is opposite to
the direction of variation of the magnetic field that generates.
I designed an experiment that should
provide the student of the early years of graduation, either in the Calculus
course, physics, or any of the modalities of engineering courses, the
capability to see the mathematical principle with the physical events that it
entails. With that aim, I’ve used a copper billet thick enough to ship the
maximum magnetic flux lines of a neodymium magnet with 3.5 cm in diameter and 1
cm of height with the form of a coin. The two pieces are used to work together
with a support base and a support rod. The base was constructed with polyester,
and serves to raise the billet metal base. We can remove the magnet that falls
within your center hole, too. The base also has a lighting system for the dowel
hole of the display, an LED with a switch on its side, and a battery cell (2 X
1.5 V). The base also has a rod serving to attach a transparent PVC pipe,
aligned with the center of the copper’s billet hole. The tube is used to guide
the fall of the magnet into the hole and has a height sufficient to one visualize
the speed fall of the magnet moving to the bottom. This action arises from the
magnetic force generated by the voltage induced in the billet of copper by
varying the magnetic field due to the fall
of the magnet. The abrupt damping of the magnet droping is caused by the rapid variation
of the magnetic flux in the time. This rapid change of the flux also generates a force proportional to the
flux variation. The force brakes the
magnet fall and prevents it fall down pulled by gravity (g = 9,81m /s2).
It was also installed along the billet a copper coil, in order to sent many magnetic
field lines, generated by the magnet to pass through the bore copper billet
The a force against the electromotive coil
is analogous to the electromotive force induced inside the billet. One cannot
measure directly this force. An oscilloscope is placed in the outer coil
terminals to measure the output voltage of the coil. A voltage pulse occurs when
the magnet enters into the coil and another when it gets out it. The magnitudes
of the pulses depend on the magnet polarity. By changing the side of the magnet
it will change the form of the wave, from a negative wave to a positive one. When
the magnet is fully inside the billet there are not cut off flux lines. Then,
no voltage arises from the movement of the magnet. The magnet falls slowly, it
which can be explained by Fleming's rule. An upward force is created, causing
the magnet to slow down during its fall, and the greater his fall, the stronger
the reaction force that will counteract its fall. This opposing force that
arises is the negative sign that has been introduced into the Lenz’s formula.
But again at the output the down hole, the
situation changes, which causes that the
contributions of a pole are greater than the contribution of the other,
generating another pulse-voltage again. Repeating the situation of the
entrance, but in reverse! Students can view the entire meaning of the Faraday
equation, by the visual experience
presented.
Vote here: https://transmitter.ieee.org/diy/share?code=1f481&show=share
See this project at Youtube: https://youtu.be/pbHr6igz22g
