Two identical conducting spheres are separated by a fixedcenter to center distan

Question

Two identical conducting spheres are separated by a fixedcenter to center distance of 43.0 cm and have different charges.Initially, the spheres attract each other with a force of 0.0988 N.The spheres are now connected by a thin, conducting wire. After thewire is removed, the spheres are positively charged and repel oneanother with a force of 0.0301 N. Calculate the final charge on thespheres. Calculate the initial charge on the sphere whichcarried a positive charge. Calculate the initial charge on the sphere whichcarried the negative charge. Two identical conducting spheres are separated by a fixedcenter to center distance of 43.0 cm and have different charges.Initially, the spheres attract each other with a force of 0.0988 N.The spheres are now connected by a thin, conducting wire. After thewire is removed, the spheres are positively charged and repel oneanother with a force of 0.0301 N. Calculate the final charge on thespheres. Calculate the initial charge on the sphere whichcarried a positive charge. Calculate the initial charge on the sphere whichcarried the negative charge.

Explanation / Answer

Let the initial charge on 1 st sphere be q and 2 nd sphere be q ' then before connected to conducting wire : ------------------------------------ Force F = K q q ' / r ^ 2       q q' = F r ^ 2 /K                where r = distance = 43 cm = 0.43 m            = ( 0.0988 * 0.43 ^ 2 ) / ( 8.99 * 10 ^ 9 )            = - 2.032 * 10 ^ -12     ----(1)        Since they areattracted After connected to conducton wire : ------------------------------------ Force F ' = K [( q + q ' ) / 2] ^ 2 / r ^ 2              = K ( q + q ' ) ^ 2 / (4 r^ 2) ( q+ q' ) ^ 2 = 4 F ' r ^ 2 / K                     = [ 4 * 0.0301*0.43^ 2 ] / [ 8.99 * 10 ^ 9 ]                     = 2.476 * 10 ^-12            ----( 2) q + q ' = 1.573 * 10 ^-6          ---(3) from eq ( 1) and ( 2) , ( q - q ' ) ^ 2 = ( q + q ' ) ^2 - 4qq'                                                       = 2.476* 10 ^ -12 - [-8.128* 10 ^ -12 ]                                                       = 10.604 * 10 ^ -12                                         q - q ' = 3.256 * 10 ^ -6   ----( 4 ) add eq ( 3 ) and ( 4 ) we get    2q= 4.829 * 10 ^ -6                                                 q = 2.4145 * 10 ^ -6 C eq (3) - eq ( 4 ) ==> 2q' = -1.683 * 10 ^ -6 C                                      q ' = -0.8415 * 10 ^ -6 C

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