# AP Physics 2: 1.4 Systems Interactions and Changes

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?

AP | AP Physics 2 |

AP Physics 2 | Systems Interactions and Changes |

Language | English Language |

Test Prep | AP Physics 2 |

### Transcript

resourceful road wonders if she could help generate electricity by running

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

going to worry about the minus sign for now.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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