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Of the charge Q on a tiny sphere, a fraction @ is to be transferred to a second , nearby sphere. The spheres can be treated as a particle What value of @ maximizes the mag F of the electrostatic force b/w the two spheres???
hi, let @ fraction is transferred to other sphere , charge on the other will be = Q@ charge remained on the first one = Q -Q@ = Q(1-@) force between the spheres , F = = k . Q@ * Q(1-@) / r^2 let k / r^2 be another const k2 F = k2 Q@ * Q(1-@) dF/d@ = k2 . Q^2 ( 1 - 2@) d^2 F / d@^2 = k2 . Q^2 ( - 2) so for a max. put dF/d@ = 0 gives , @ = 1/2 for this d^2 F / d@^2 is also <0 so for @ =1/2 we will have max. force
hi,
let @ fraction is transferred to other sphere , charge on the other will be = Q@
charge remained on the first one = Q -Q@ = Q(1-@)
force between the spheres , F =
= k . Q@ * Q(1-@) / r^2
let k / r^2 be another const k2
F = k2 Q@ * Q(1-@)
dF/d@ = k2 . Q^2 ( 1 - 2@)
d^2 F / d@^2 = k2 . Q^2 ( - 2)
so for a max. put dF/d@ = 0
gives , @ = 1/2
for this d^2 F / d@^2 is also <0
so for @ =1/2 we will have max. force
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