Two identical charged spheres are suspended from a common point by massless strings of length l, initially at a distance d(d≪ l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with velocity v. Then v varies as a function of the distance x between the spheres as:
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When charge varies uniformly with time, combine
F∝ (q²)/(x²)
with small-angle approximations to find velocity–distance relations.