ShmoopTube

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here's your shmoop du jour brought to you by hamsters. hamsters love

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running on hamster wheels. running as fast as they can without actually going [hamster running on wheel]

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anywhere. there's probably a poetic metaphor about life in there somewhere

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but this isn't AP English so let's get to the physics. Maggie the hamster over

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hears is a news report about the search for new sources of energy. the

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resourceful road wonders if she could help generate electricity by running

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really fast around the wheel in her cage. to test the idea Maggie attaches a

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magnet to a point on her wheel and places a coil of wire with a hundred

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turns above the wheel. with each full rotation of the wheel the change in

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magnetic flux through the coil is 0 point 5 times 10 to the negative fourth

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Weaver's. the wheel spins at an angular frequency of 12 radians per second.

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calculate the electromotive force induced in the coil of wire for one full

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rotation of the wheel, and here are the potential answers.well maybe this

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is the answer we've been looking for. hamsters could solve the world's problem. [hamster wears goggles]

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a power plant could just be filled with hamsters running on wheel 24 by 7. sure

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they might not generate enough power to charge an iPhone, but there are cuter

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than a lump of coal . to solve this equation we need to know Faraday's law.

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well Faraday's law states the magnitude of the induced electromotive force

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equals the number of coils, n, times rate of change of magnetic flux. oh and

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there's a negative sign that goes at the front because of Lenz law. alright well

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that's because EMF is generated creates a current in the coil which creates its

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own magnetic field that opposes the change in flux of the field of the

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magnet acting on the coil. the minus sign works to tell us the direction the

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current needs to move in order to create a magnetic field that opposes the change

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in flux of the magnetic field from the magnet on Maggie's wheel. in this [hamster wheel powers light bulb]

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question though we're just looking for the magnitude of the force independent

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of the direction so our answer will be positive. got all that? and we're not

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going to worry about the minus sign for now.

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alright long way to go just get back to where we started. but the only reason we

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get to ignore the minus sign is because we're looking for the scalar magnitude

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of the EMF .any other time we need to keep it in there .after all is the law.

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okay so we know the equation will use to solve this but we're still missing a

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variable namely the change in time or delta T. we need to know how much time it

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takes for the wheel to make one rotation. well thats related to the angular

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frequency angular frequency. equals 2pi over time. so we can solve for time which

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equals 2pi over angular frequency. and we'll round by down to three to make a

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life of a lot easier. the question gives us the angular frequency so we know it's [equation]

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12 radians per second .plugging in the numbers we find that the change in time

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equals 0 point five seconds .now we have everything we need to solve this and see

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if Maggie is the solution to the energy crisis. the EMF created 100 coils times

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the change in magnetic flux, point five times ten to the negative fourth levers

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over the change in time, point five seconds, and that gives us an answer of

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point 01 volts. so the correct answer is a. it looks like Maggie isn't going

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to replace fossil fuels anytime soon but that's to be expected, besides we

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wouldn't want to give hamsters that much control over our power supply ,they seem

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cute now but all that power could go over their little rodent heads. [hamsters picketing]

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