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**Electromagnetic Induction**

Electricity from Magnetism

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Induced Current When a conductor is moved in a magnetic field, current can be induced (caused) Faraday’s Original Experiment

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**Many Ways to Produce EMF**

Many forms of changing magnetic field can produce Emf (current) Magnet or coil or both can move Field can turn on or off due to closing or opening a switch

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Faraday’s Law (I) Induced emf is proportional to the rate of change of magnetic flux FB passing through a loop of area A FB = BAcosq q is angle between B and a line perpendicular to the face of the loop Flux applet Courtesy Dept. of EE Surrey University

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**Nature of Magnetic Flux**

FB = BAcosq is a scalar Above formula comes from “dot product” of B and A whereas F =Bqvsinq comes from “cross” or vector product B x v Unit of magnetic flux is tesla-meter2 or weber

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**Ways of Changing Flux Move coil into or out of field**

Change area of coil Rotate coil so number of field lines changes Change field strength Ways Flux will not change Rotate coil around field line – doesn’t change number of field lines Slide coil at constant angle within field

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**Faraday’s Law (II) Emf = -N D FB/ Dt**

Magnetic flux is also proportional to total number of field lines passing through loop When q = 00 magnetic flux FB = BA (A is area of loop perpendicular to magnetic field) When q = magnetic flux is zero; no field lines pass through loop. Mathematically Emf = -N D FB/ Dt N is number of loops

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Almost calculus D FB/ Dt is time rate of change of flux

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Simple example A square loop of side a enters a region of uniform magnetic field B in time Dt = one second. Write an expression for the voltage induced during that interval Emf =-N D FB/ Dt = -a2B/1 second =-a2B

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Current direction? How do we know in what direction, clockwise or counterclockwise the induced current will flow? Energy conservation plays a role Energy in the current and voltage must come from somewhere How this works is called Lenz’s Law

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Lenz’s Law Minus sign in Faraday’s Law reminds us that Induced current produces its own magnetic field This field interacts with original field to make a force Work must be done against this force to produce induced current or conservation of energy will be violated An induced emf always gives rise to a current whose magnetic field opposes the original change in flux Applet

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How Current Varies Link (demonstrates Lenz’s Law with bar magnet and loop)

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In Other Words Physical motion that induces current must be resisted by magnetic forces Something has to do work to induce the current, otherwise energy conservation is violated

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**What is Direction of Current?**

loop Current clockwise Field in this region toward us

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**What is Direction of Current?**

loop Field in this region away from us Current counter clockwise

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**Changing Area – What is the direction of induced current?**

Field away from us xxx Field toward us Answer to CW. Induced field away to restore existing field Answer to 2. CCW. Field toward us to restore existing field Loop area shrinks

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**What if Loop Area Increases?**

Answers reverse 1 CCW 2 CW

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**Another Example of Lenz’s Law**

When field is increasing, induced field opposes it When field is decreasing, induced field acts in the same direction Diagram courtesy Hyperphysics web site

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**Example: Square coil side 5. 0 cm with 100 loops removed from 0**

Example: Square coil side 5.0 cm with 100 loops removed from 0.60T uniform field in 0.10 sec. Find emf induced. Find how flux FB = BA changes during Dt = 0.10 sec. A = Initial FB Final FB = zero Change in flux is Emf = -(100)(-1.5 x 10-3 Wb)/(0.10 s) = 2.5 x 10–3 m2 1.5 x 10-3 Wb -1.5 x 10-3 Wb 1.5 volts

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Example, continued If resistance of coil is 100 ohms what are current, energy dissipated, and average force required? I = emf/R = 1.5v/100 ohms = E = Pt = I2Rt= F = work required to pull coil out/distance = energy dissipated in coil/distance = W/d = 15mA 2.25 x 10-3 J 0.050 N Use d = 0.05 m since no flux change until one edge leaves field

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**EMF in a Moving Conductor**

Courtesy P Rubin, university of Richmond

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**Moving Rod Changes Area of Loop**

Let rod move to right at speed v Travels distance Dx = v Dt Area increases by DA = LDx=L v Dt By Faraday’s law Emf = D FB/ Dt = BDA/Dt = BLvDt/Dt = BLv B, L and v must be mutually perpendicular

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**Alternate Derivation of emf = BLv**

Force on electron in rod moving perpendicular to magnetic field strength B with speed v is F=qvB acting downward Produces emf with top of rod + CCW conventional current as rod slides to right Work to move a charge through rod against potential difference is W = Fd = qvBL. Emf is work per unit charge BLv

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**Blv Example: Voltage across an airplane wing**

Airplane with 70 m wing travels 1000 km/hr through earth’s field of 5 x 10-5 T. Find potential difference across wing. Is this dangerous? Emf = Blv = Could such a potential difference be used to reduce the aircraft’s need for fuel? (5.0 x 10-5 T) (70m) (280 m/s) = 1.0volt

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The Generator Generators and alternators work by rotating a coil in a magnetic field. They produce alternating current.

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