# AP Physics 2: 2.4 Systems Interactions and Changes

AP Physics 2: 2.4 Systems Interactions and Changes: Determine the radius R1.

AP | AP Physics 2 |

AP Physics 2 | Systems Interactions and Changes |

Language | English Language |

Test Prep | AP Physics 2 |

### Transcript

collected a charge of eight coulombs on a metal sphere of a radius R sub 1 he

has an out-of-town gig and wants to take some of the charge with him he connects

his sphere to another sphere with a thin conducting wire the second sphere has a

radius of 12 centimeters and its uncharged before the connection take a

look the following diagram right here now once the system has reached [diagram of two spheres]

equilibrium the charge on sphere 2 is fixed Coulomb determine the radius R of

the first sphere and here the potential answers... Okay well in the 1730's this was [woman using her mouth to throw a chair in the air]

cutting-edge entertainment never been so glad to not live in 1730's but we're sure

seeing electricity in action for the first time back then was well pretty mind [man staring at a blank TV screen]

blowing. When the two spheres reach equilibrium the surfaces of each will

have the same electric potential at a spheres surface and farther out the

electric potential will be equivalent to that of a point charge located at the [finger pointing to the center of a sphere]

center of the sphere well that potential equals the amount of charge over 4 pi

times the electric constant times the radius since we're dealing with the

system after the spheres have reached equilibrium, their voltage will be the

same and so we can set the voltage equations for each sphere as equal also [Two voltage equations for each sphere]

we can cancel out that hole 4 pi electric constant jibber-jabber and just

find that charge one over radius 1 equals charge 2 over radius 2 which

means that the radius of the first sphere equals the radius of the second

sphere multiplied by the first charge over the second charge now because a little

something called the law of conservation of charge we know that the total charge [law of conservation of charge drawn on a table]

in the system has to remain the same the total charge equals the charge on the

first sphere before there was any transfer we can use that second equation Q sub 1

equals Q sub t minus Q sub 2 in the equation we just

saw for the radius and then we can plug in our numbers our sub 1 equals 12

centimeters times 8 coulombs minus 6 coulombs over six coulombs and that means

the radius of the first sphere equals four centimeters so the correct answer [equation for the radius of a sphere]

is B.. and remember if you're going to be an electrical entertainer well be careful

you don't want the people to be entertained by your pain [Sparky being electrocuted on stage]