The units on the right side of this equation are the product of the units of magnetic field B (in teslas) and area A (in meters2), which is defined to be the units of magnetic flux ΦB, in T·m2 or webers.
(There is a similar construct of electric flux ΦE (defined as the measure of electric field lines passing through a surface) that we have omitted from our discussion of electromagnetism. As it turns out, what happens to the magnetic flux ΦB is a much richer topic in terms of practical applications, such as building generators and other devices.)
The amount of induced emf can be compounded by the number of coil turns N in the wire loop. If there are more turns, then there is a proportional increase in the induced emf, for a given change in magnetic flux.
The main idea of Faraday's law is that in order to induce an emf in a wire loop (such that current begins to flow), the magnetic flux ΦB must somehow be changed.
(The negative sign on the right side of this equation is explained by Lenz's law later in this presentation.)
In the slide-rail generator, we have a rod moving to the right, along rails that complete a circuit, in the presence of a magnetic field that points into the plane of this page. In our previous discussion, moving the rod creates an induced emf in the rod itself, which induces current in the rest of the rod-rail circuit. The faster the rod moves, the more induced emf (and current) is produced; for a stationary rod there is no induced emf (and current).
In terms of Faraday's law, we simply note that the amount of area enclosed by the rod-rail circuit that magnetic field lines passes "through" increases steadily as the rod is moved to the right. This means that there is more and more magnetic flux ΦB (as the area increases in ΦB = B⊥·A), which creates an induced emf (and current) in the rod-rail circuit. The faster the rod moves, the faster increase there is in area and flux, and the more induced emf (and current) is produced; for a stationary rod, there is no change in area and flux, so there is no induced emf (and current).
First, recall from a previous presentation how the third right-hand rule (RHR3) relates the magnetic field created by the current in a wire loop. Keep in mind that is the magnetic field created by the induced current in the wire loop, and not the external magnetic field that is responsible for the constant/changing magnetic flux ΦB that passes "through" the loop.
However, the current induced in a loop (because the external magnetic flux through it is changing over time) will be in the direction that creates a magnetic field that opposes the changes in the external magnetic flux. If the flux through the coil is increasing because the external magnetic field lines are getting stronger, then the resulting induced current in the coil will "fight" this change by creating magnetic field lines in the opposite direction, to "cancel" out the strengthening external magnetic field. If the flux through the coil is decreasing because the external magnetic field lines are getting weaker, then the resulting induced current in the coil will "fight" this change by creating magnetic field lines in the same direction, to "boost" the weakening external magnetic field.
How does the coil "know" the direction that the induced current must flow in order to resist changes in the external magnetic field? Consider trying to change the motion of a heavy brick, by increasing its speed by throwing it, or decreasing its speed by catching it--how does the brick "know" how hard and which direction to press back on you as you try to speed it up, or slow it down? The brick doesn't really know, but it is merely resisting changes in its motion due to its mass (which Newton's law is that?). In an analogous manner, the coil doesn't really know which direction the induced current should flow, it is merely resisting changes in its magnetic flux...and that is Lenz's law.
For purposes of this discussion, we can personify the coil as "hating change," such that the current induced in it "kills" or "boosts" increasing or decreasing flux through it.
The clip at the beginning of this presentation has a similar set-up, where there is large coil in the pedestal where current is ramped up and down rapidly, creating a changing magnetic field. This creates a continuously changing magnetic flux through the aluminum plate (effectively a coil or loop), and we can see how the induced currents in the plate continuously "fights" the changing external magnetic field of the pedestal as it levitates in the air. Also the light bulbs in the chandelier are also effectively coils that have currents induced in them due to the changing magnetic flux from the pedestal, which makes the bulbs light up.
Next time turn on your blender next to your radio. While the rapidly changing currents in your blender won't levitate your radio, it will cause the magnetic flux to continuously change through your radio circuitry, inducing currents that will be picked up as rude static.
(Keep in mind that these are all time-averaged values, which seem constant, but the instantaneous values of voltages and currents are all continuously changing per time.)
(Note that the battery only provides a direct current, which by itself could not vary the primary coil magnetic field, and not vary the magnetic flux through the secondary coil, so there would be no induced emf in the secondary coil. However, an oscillating circuit will rapidly vary the otherwise direct current from the battery, and the resulting abrupt changes in the current in the primary coil then can create a fluctuating magnetic field and a fluctuating magnetic flux through the secondary coil, which has more windings, and thus a corresponding stepped-up emf. In practice, salvaging these circuits from disposable cameras should be exercised with caution, due to the amount of charge that can be stored in the capacitors within.)
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