3 - Faraday's Law, Lenz's Law and the Lorentz Force

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Faraday's Law

The fact that a changing magnetic field induces a current to flow was credited to Faraday. Faraday's Law says that when the strength of a magnetic field changes within a loop of wire, a current will flow whose magnitude depends on the rate of change of the magnetic field.

Related to the current induced in a loop of wire by a changing magnetic field, Lenz's Law says that the direction of the current that is induced is such that it produces its own magnetic field in a manner that opposes the original magnetic field.

We saw striking demonstrations in the Sprott video of the consequences of Faraday's and Lenz's Law:

• Crushing Tin Can: A coil of wire is place around a tin can. Then a very large current flow rapidly through the coil. This current creates a large rapidly changing magnetic field. This changing magnetic field, in turn, induces a current in the metal of the can according to Faraday's Law. Next, according to Lenz's Law, the induced current sets up its own magnetic field whose direction opposes that of the coil wrapped around the can. These clashing fields produce forces on the can which crush it.
• Repelling Metal Ring: In another demonstration, Sprott placed a metal ring on top of another coil of wire. As in the crushing can experiment, a large rapidly changing current goes through the coil of wire. Lenz's law explains why the metal ring flies upward. The current induced in the ring produces a magnetic field that opposes the field in the coil. It is like two magnets with like poles facing each other. The two magnetic fields repel each other.

So far we have discussed only in a qualitative way that charged particles may be made to flow by by changing magnetic fields. But we also find that a moving particle may experience a force on it due to a magnetic field. We now give the rule that expresses the force (F) on a particle of charge (q) that has velocity (v) perpendicular to a magnetic field (B). This is the Lorentz force. Its direction is perpendicular to both v and B there is a "right hand rule" that tells you how to get the relative directions between F, v and B. All of this is nicely demonstrated on the website above where both a positive charge and a negative charge with velocity v perpendicular to a constant magnetic field are seen to go in a circle. Note first the units.
F(Newtons) = q(Coulombs)v(m/s)B(Tesla)

Defining The Ampere: The unit of current, the ampere, is based on a measurement of the force between two long parallel wires each carrying the same current. How does this work? Note that if a wire with a current produces a magnetic field around it, a magnet in the vicinity of the wire will be attracted by the magnetic field of the wire. But since another wire with a current in it produces its own magnetic field, one may infer that the magnetic field of one wire attracts the magnetic field of the other wire. Hence, if two long parallel wires with the same current in each wire are 1 meter apart and they experience a force of 2x10^-7 N per each 1 meter length of the wire, the current in each wire is said to be one ampere. Likewise, the amount of charge passing each point in the wire in one second is one coulomb.

Defining the Magnetic Field Strength: The magnetic field that surrounds a long straight wire at a distance of one meter from the wire is 2x10^-7 Tesla. Also, 1 Tesla = 10,000 Gauss .