Physics 21: 1-5 Induced Current
- 21.1 By the beginning of the nineteenth century, physicists knew there was a connection between magnetism and electrical phenomena. Ampère had determined how large a magnetic field was produced by current in a wire. Faraday then measured the current in a wire coil induced by a moving magnet. Faraday envisioned the strength of the electrical field or magnetic field as a kind of flow of force through a cross-section area, which he called flux and which we now symbolize with ΦE or ΦB.
- 21.2 Faraday's law of induction: Only when the flow is changing does a potential capable of inducing current arise, and then it is proportional to the change: ΦB = BA cos θ. The induced electrical flow (emf Ɛ) is a result of the change in magnetic flux ΦB over time, and, following the conservation of energy laws, flows in such a direction that the magnetic field that results from its own flow opposes the magnetic change that induced it. So we have an initial magnetic flux with B and ΦB in one direction inducing a current flow that itself creates a magnetic flux ΦB' in the opposite direction (Lenz's law). Those of you who have taken chemistry may recognize a similar phenomena in Le Chatelier's principle: when a chemical system in equilibrium is disturbed, the chemical reaction will run in a direction to reduce the disturbance and establish a new equilibrium. Both behaviors are a result of conservation of energy.
- 21.3 It doesn't matter how flux is generated. A wire loop will experience a change in magnetic flux if we move a magnet near it, if we move the loop into or out of a stable magnetic field, or if we change orientation of the area enclosed by the wire loop to the local magnetic field. In all these cases, as long as something is moving (the magnet, the loop), ΦB will be changing. Electrons in the loop will experience a force F = qv ⊗ B = qvB sin θ as the bar of the loop moves with velocity v through the magnetic field B. When v is at right angles to B (v ⊥ B), θ = 90°, sin θ = sin 90° = 1, and the magnitude of F becomes qvB, with the direction given by the right-hand rule. When the wire moves a distance l, the work done by this force is W = qvB * l. The Ɛ is the work per charge, so Ɛ = W/q = qvBl/q = vBl.
If we approach the same situation from an analysis of the magnetic flux definition of emf Ɛ, we get the same answer (see analysis below).
- 21.4 Since we have an EMF and a current, we have an electrical field. A changing magnetic field induces an electric field.
- 21.5 Michael Faraday's work with induced electrical current lead him to realize that just as an electrical motor can use electrical current to do mechanical work, mechanical work (when it spins a magnet) can generate electrical current. By properly setting up the magnet and coils, a generator can produce direct current (DC), and in a slightly different configuration, and alternator can produce alternating current (AC). Any source of mechanical energy can be used to turn the magnet. In the United States, steam power from burning coal or nuclear power plants can be used or water power is not available.
Alternating current can be generated by a dynamo or spinning magnetic system; in many places, hydroelectric power is generated by using falling water to provide the mechanic force necessary to rotate an armature. Alternators use the mechanical spin of the engine to recharge car batteries.
||Flux is determined from the amount owed magnetic field passing through "surface" area in a direction perpendicular to the plane of the area. Flux is always "normal" to the area.|
|Faraday's Law of Induction||
|| Remember that emf Ɛ is not a force. It is the potential difference between two terminals of any device that transforms some other type of energy (chemical, mechanical) into electrical energy. When the electrical source is a battery, Ɛ is the voltage of the battery. When the electrical source is a changing magnetic field, the magnitude of the resulting Ɛ through a single loop of wire depends on the rate at which the magnetic field (as measured by its flux through the area enclosed by the wire) is changing. If we have multiple loops of wire, the induced Ɛ through each wire is the same; so we can increase the net Ɛ by coiling the wire many times. |
|Lenz's law||Determines direction of current flow from Ɛ||The direction of the induced Ɛ will create a magnetic field that opposies the original change in flux.|
|Electric field induced by magnetic field||
||The field induced by a charge moving through a magnetic field depends on its velocity|
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