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Motors Physics 102 Professor Lee Carkner Lecture 21

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Ring in Solenoid To get maximum flux, the ring should face up (parallel with the coils) We need to find the flux through the loop before and after the current is switched off = BA cos = BA B = 0 nI = (4 X10 -7 )(1000)(10) = A = (0.1)(0.1) =

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Current in Ring = BA = (0.0126)(0.01) = In 1 second the flux goes to 0 = (1.26 X 10 -4 ) - (0) = 1.26 X 10 -4 t = 1 = -N( / t) = (1)(1.26 X 10 -4 ) = V = IR or I = /R = 1.26 X 10 -4 /10 I =

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Lenz’s Law

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Direction of Current (PAL) If the solenoid has clockwise current what is direction of induced current? The flux goes from down to zero Ring tries to counteract change and get original flux back

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Motional emf Instead of changing the magnetic field, what if we change the loop? called motional emf How does motion in a field translate to voltage?

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Induced Potential Suppose we have a straight wire moving in a magnetic field We can relate the deflection force to the electric force qE = qvB or E = vB Since V = Ed, if L is the length of the wire: Potential induced in a wire of length L moving at velocity v through a magnetic field B

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Motional emf - Derived The area of the loop increases by L x in time t / t = (BL x)/ t = N( / t) = BLv X B field into page v x L x in time t

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Motional emf -- Direction If the area decreases, the flux decreases and thus the induced B field is in the same direction as the original

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Generators What is the best way to use inductance to produce current? This changing flux produces an emf in the loop Falling water, rising steam etc. Generator converts work into emf

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Alternating Current Which way does the current flow? Thus the current flows in one direction and then the other e.g. household current is at 60 Hz, or 60 cycles per second This is called alternating current

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emf From a Generator Consider a loop of wire rotating in a magnetic field with angular speed From Faraday’s Law: The flux is equal to BA cos The change of with time is thus BA sin t, so the emf is: = NBA sin t

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Frequency How does the emf vary? As the loop makes one complete rotation ( goes from 0 to 2 radians) the emf goes from 0, to maximum +, to maximum -, and back to zero again 1 turn per second (f=1) means 2 radians per second ( =2 ) max

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Today’s PAL Consider a generator that consists of a single 1 meter by 1 meter loop of wire with a resistance of 15 in a magnetic field of 2 T How many times per second must you rotate the loop to produce a maximum current of 12 amps?

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Power Generation Produced (in general) in two ways: Chemical reactions separate charges so that one terminal is + and one is - A changing magnetic field separates charges

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An Alternating Current Generator

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Motors If you run a generator backwards it becomes a motor Motor converts emf to work This reduces the emf of the loop and is called back emf Example: A motor initially has 120 volts, but if the motor produces a back emf of 70 volts, then the total emf is 50 volts

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Force on Eddy Curents

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Eddy Currents As the field through the loop drops, it induces a field in the same direction If the object is not a loop, circular currents can still be induced which have the same effect Net effect: Metal objects moving through a magnetic field will be slowed

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Next Time Read 21.7, 21.9-21.11 Homework: Ch 21, P 14, 23, 30, 39

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