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Electricity and Magnetism Electromagnetic Induction Mr D. Patterson

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Outcomes describe and apply the concepts of magnetic flux and magnetic induction—this will include applying the relationships: describe the production of an induced emf by the relative motion of a straight conductor in a magnetic field—this will include applying the relationship:

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An electric motor uses electricity to produce movement An electric generator uses motion to produce electric current

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Simple example

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Explanation Electric charges cutting across magnetic field lines will feel a force The conductor must be moving perpendicular to the magnetic field V

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Emf The separation of charge is similar to a battery An EMF is produced! No current however as the “battery” is not connected to a circuit V

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Current If there is a complete circuit the EMF will force a current to flow. This process of generating an electric current using a magnetic field is called electromagnetic induction. “An EMF is induced in the conductor” “The induced current flows through an external circuit” V

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Formula The EMF induced in a conductor: ε is the EMF (V) l is the length of the conductor (m) v is the velocity of the conductor (ms -1 ) B is the magnetic flux density (T)

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Magnetic Flux The magnetic flux is a measure of the total magnetic field in a given area is the magnetic flux (Wb) B is the magnetic flux density (T) A is the perpendicular area (m 2 )

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Faraday’s and Lenz’s Law Faraday’s Law: The induced EMF in a single coil is equal to the negative rate of change of magnetic flux through that coil

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There are multiple ways to Induce an EMF

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Lenz’s Law Lenz’s Law: An induced current will create a magnetic field which opposes the change in magnetic field that created the current This is the reason for the negative sign in the formula

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Using the right hand rule with Lenz’s Law For a straight conductor: Swap the direction of the magnetic field to find the induced current V

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Using the right hand rule with Lenz’s Law For a coil: Create a magnetic field inside the coil which is opposite to the changing magnetic field OR create a magnet inside the coil whose poles will resist the motion of the external magnet

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Using the right hand rule with Lenz’s Law If a magnet is stationary in (or near) the coil, there is no change in flux, so no induced EMF or current

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Using the right hand rule with Lenz’s Law For a coil: Create a magnetic field inside the coil which is opposite to the changing magnetic field OR create a magnet inside the coil whose poles will resist the motion of the external magnet

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Size of the induced magnetic field depends on size of the induced current NNN Large resistance Small resistance No resistor (Infinite resistance)

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Example Problem A square coil is free to rotate about its central axis and is perpendicular with an external magnetic field. The coil rotates 90 deg until it is parallel with the field in 12.0 ms. The external magnetic field has a flux density of 850 mT. a) What is the initial magnetic flux passing through the coil? b) What is the final magnetic flux passing through the coil? c) What is the average EMF produced from the rotation? d) Will the reading on the ammeter be positive or negative? + A - 8.50 cm

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