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.

Lenz's Law

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:

Lorentz Force

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)

Forces Between Parallel Wires

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 .

R.S. Panvini