ShmoopTube

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And here's your shmoop du jour brought to you by electrical

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entertainment rumor has it that there are ways to be entertained that don't [man sitting on a couch watching television]

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involve electricity but that involves scary things like activities that are

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done outside ooh sounds gross we'll stick with cat videos all right, sparky

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the shocker is the star electrical entertainer act of the 1730's parties [Sparky on stage holding a positive and negative balls]

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

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

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

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

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

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

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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]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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