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AP Physics 2: 1.4 Systems Interactions and Changes. What is the electromotive force induced in the coil of wire for one full rotation of the wheel?

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Transcript

00:00

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

00:08

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

00:12

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

00:15

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

00:20

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

00:25

resourceful road wonders if she could help generate electricity by running

00:29

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

00:33

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

00:37

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

00:42

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

00:46

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

00:52

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

00:56

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

01:02

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

01:06

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

01:11

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

01:14

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

01:18

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

01:23

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

01:30

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

01:34

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

01:37

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

01:42

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

01:47

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

01:51

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

01:56

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

02:00

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

02:03

going to worry about the minus sign for now.

02:05

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

02:09

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

02:13

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

02:17

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

02:21

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

02:27

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

02:31

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

02:37

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

02:41

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

02:47

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

02:51

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

02:56

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

03:01

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

03:05

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

03:10

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

03:15

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

03:19

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

03:23

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

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