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Understanding Faraday's LawElectromagnetic Induction from Changing Magnetic Flux
A changing magnetic field will induce an electric current and corresponding electric potential difference according to Faraday's Law of electromagnetic induction.
Electrical and magnetic phenomena are intimately connected and cannot be separated. Physicists however did not always understand the connection. In the early 19th century physicists suspected that electric and magnetic phenomena were related, but had not yet found the connection. In 1820 Hans Christian Oersted discovered part of the connection when he found that electric currents induce magnetic fields. Michael Faraday and Joseph Henry independently discovered the reverse connection in about 1830. A changing magnetic flux induces an electric potential difference, commonly called voltage, that can cause an electric current. Induction ExperimentsA galvanometer or ammeter can detect small electric currents. Wrap a few coils of wire around a bar magnet; more coils increase the effect. Hook the ends of the wire to the terminals of the meter. It will detect no current. However sliding the magnet in or out of the coils of wire will produce a current. Rotating the wire coils in a magnetic field will also produce a current. Notice that the magnetic field only induces a current if the total amount of magnetic field through the area enclosed by the coil of wire changes, either by rotating the coil or moving the magnet. Magnetic FluxUnderstanding Faraday's law requires understanding the concept of magnetic flux. The magnetic flux is a way of measuring the total amount of magnetic field over a surface or a surface area. An example might be the area of the coil of wire in the above experiments. If the magnetic field direction is perpendicular to the surface, then the magnetic flux is the magnetic field multiplied by the surface area. If the magnetic field is not perpendicular, then this product must also be multiplied by the cosine of the angle between the magnetic field direction and the outward pointing line perpendicular to the surface. This line perpendicular to the surface is called the normal. In equation form the magnetic flux is given by: Phi = BA cos (theta) Phi is the magnetic flux. B is usually called the magnetic field but is more properly called the magnetic induction. A is the total area, and theta is the angle between the magnetic field direction and the normal to the surface. Faraday's LawBy doing quantitative experiments similar to those above, Faraday found that the induced voltage, which is also called the electromotive force, in a single coil of wire equals the negative of the change in magnetic flux divided by the change in time. If there is more than one loop of wire, then this result is multiplied by the number of loops of wire in the coil. In equation form Faraday's law is expressed as: Emf = - N (Delta Phi)/(Delta t) or using calculus notation: Emf = -N dPhi/dt Emf represents the induced voltage or electromotive force and N is the number of loops of wire. Delta Phi represents the change in the magnetic flux; Delta t is the change in time. In the calculus form of the equation dPhi/dt is the derivative of the flux with respect to time. The negative sign gives the direction of the induced voltage. According to Lenz's law the induced current or voltage must be in a direction so that it opposes the change that induced it. Faraday's law along with Oersted's discovery, Ampere's law, and Gauss's law led to our understanding of electromagnetic phenomena that culminated with Maxwell's brilliant synthesis. Further ReadingHecht, E., Physics:Algebra/Trig, Brooks/Cole, 1997. Knight, R.D., Physics for Scientists and Engineers with Modern Physics, Pearson, 2004. Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.
The copyright of the article Understanding Faraday's Law in Electricity & Magnetism is owned by Paul A. Heckert. Permission to republish Understanding Faraday's Law in print or online must be granted by the author in writing.
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