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To small equally charged spheres each of mass m are suspended from the same point by silk threads of length L. The distance between the spheres x lt lt L. Find the rate (dq)/(dt) with which he charges leak off each sphere if their approach velocity varies as vartheta =(a)/(sqrt(x)) where a si a constant. |
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Answer» Solution :For momentaryequilibrium of the spheres, `T COS THETA=mg and T SIN theta = F` where Tis tensionin the STRING `rArr tan theta =(F)/(mg)` For `x lt lt L`,  we can take `tan theta =(x)/(2L)` So `F=(mg x)/(2L)` Here `F=(1)/(4pi in_(0)) (q^(2))/(x^(2)) and q^(2)=(2pi in_(0) mg x^(3))/(L)` given `(dx)/(dt) =(a) /(sqrt(x))` where a is a constant `rArr (dq)/(dt)=(3q)/(2)sqrt((2pi in_(0) mg)/(L))` |
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