Lenz's Law and Faraday's Law of Induction
1. With this definition of the flux being , we can now return to Faraday's investigations. He found that the magnitude of the emf produced depends on the rate at which the magnetic flux changes. Faraday found that if the flux through
N loops of wire changes by an amount , during a time delta t, the average induced emf during this time is
This fundamental result is known as Faraday's law of induction.
The minus sign is placed there to remind us in which direction the induced emf acts. Experiment shows that an induced emf always gives rise to a current whose magnetic field opposes the original change in flux. This is known a Lenz's law. Let us apply it to the case of relative motion between a magnet and a coil. The changing flux induces an emf, which produces a current in the coil; and this induced current produces its own magnet field. If the distance between the coil and the magnet decreases; so the magnetic field, and therefore the flux, through the coil increases. The magnetic field of the magnet points upward. To oppose this upward increase, the field produced by the induced current must point downward. Thus Lenz's law tells us that the current must move by the use of the use of the right hand rule. If the flux decreases, so the induced current produces an upward magnetic field that is "trying" to maintain the status quo.
Let us consider what would happen if Lenz's law were just the reverse.
The induced current would produce a flux in the same direction as the original change; this greater change in flux would produce an even larger current, followed by a still larger change in flux, and so on. The current would continue to grow indefinitely, producing power (=) even after the original stimulus ended.
This would violate the conservation of energy. Such "perpetual - motion" devices do not exist.
It is important to note, which I believe was forgotten in the class lecture, is that Faraday's investigation, as summarized in Faraday's law, says that an emf is induced whenever there is a change in flux. Thus an emf can be induced in two ways: (1) by changing the magnetic field B; or (2) by changing the area A of the loop or its orientation theta with respect to the field.
A motor turns and produces mechanical energy when a current is made to flow in it. You might expect that the armature would accelerate indefinitely as a result of applied torque.
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In this AC circuit, you can analyze that each resistor is in series with either an inductor, voltage source, or capacitor. Resistor 2 is in series with the capacitor. Resistor 3 is in series with the inductor. Resistor 1 is in series with the AC voltage source. From this, you can realize that they are now in parallel with each other once they have been in series with each other. The inductor is a coil of wire. Since we assumed the inductor is ideal, the resistance of the wire and capacitance is negligible. The voltage across the inductor has its own magnetic field. The current in the coil sets up the magnetic field. Since the inductor is ideal, it does not dissipate any energy. You have a changing current, di/dt, and it is decreasing because it is sinusoidal. In this AC circuit, there is an induced emf that is opposite of the current.
... spring, you are causing a twisting motion all the way down the coil. (Longhurst)
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V(voltage) I (current) Therefore, I = V R Therefore, if V is constant, in order to increase I, R must decrease.
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