hw1 - HOMEWORK SOLUTIONS PHY108 Fall 08(Due on 9-3 4 The...

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881 HOMEWORK SOLUTIONS PHY108 Fall 08 (Due on 9-3) 4. The fact that the spheres are identical allows us to conclude that when two spheres are in contact, they share equal charge. Therefore, when a charged sphere ( q ) touches an uncharged one, they will (fairly quickly) each attain half that charge ( q /2). We start with spheres 1 and 2 each having charge q and experiencing a mutual repulsive force 22 / F kq r . When the neutral sphere 3 touches sphere 1, sphere 1’s charge decreases to q /2. Then sphere 3 (now carrying charge q /2) is brought into contact with sphere 2, a total amount of q /2 + q becomes shared equally between them. Therefore, the charge of sphere 3 is 3 q /4 in the final situation. The repulsive force between spheres 1 and 2 is finally 2 ( / 2)(3 / 4) 3 3 ' 3 0.375. 8 8 8 q q q F F k k F r r F 5. The magnitude of the force of either of the charges on the other is given by F q Q q r 1 4 0 2 b g where r is the distance between the charges. We want the value of q that maximizes the function f ( q ) = q ( Q q ). Setting the derivative / dF dq equal to zero leads to Q – 2 q = 0, or q = Q /2. Thus, q / Q = 0.500. 7. We assume the spheres are far apart. Then the charge distribution on each of them is spherically symmetric and Coulomb’s law can be used. Let q 1 and q 2 be the original charges. We choose the coordinate system so the force on q 2 is positive if it is repelled by q 1 . Then, the force on q 2 is F q q r k q q r a 1 4 0 1 2 2 1 2 2 where r = 0.500 m. The negative sign indicates that the spheres attract each other. After the wire is connected, the spheres, being identical, acquire the same charge. Since charge is conserved, the total charge is the same as it was originally. This means the charge on each sphere is ( q 1 + q 2 )/2. The force is now one of repulsion and is given by F r k q q r b q q q q 1 4 4 0 2
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This note was uploaded on 03/26/2010 for the course PHY 108 taught by Professor Iashvili during the Spring '08 term at SUNY Buffalo.

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hw1 - HOMEWORK SOLUTIONS PHY108 Fall 08(Due on 9-3 4 The...

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