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zukkash
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Electrostatics-- spheres leaking charge
Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length d. The distance between the spheres x << d. Find the rate dq / dt with which
the charge leaks off each sphere if their approach velocity varies as v = a / √x, where a is a constant.
Coulomb's law, F = ma.
Approximating the gravity term since x << d, we can write k q^2 / x^2 - mg x / (2d) = m a. We could solve this for q and find dq / dt, etc. However, I only get the correct answer (from the back of the book) if I set a = 0, i.e. the spheres are in equilibrium as they fall toward each other. I also see the assumption of equilibrium made in other solutions of this problem on the web. Why is this assumption justified?
Homework Statement
Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length d. The distance between the spheres x << d. Find the rate dq / dt with which
the charge leaks off each sphere if their approach velocity varies as v = a / √x, where a is a constant.
Homework Equations
Coulomb's law, F = ma.
The Attempt at a Solution
Approximating the gravity term since x << d, we can write k q^2 / x^2 - mg x / (2d) = m a. We could solve this for q and find dq / dt, etc. However, I only get the correct answer (from the back of the book) if I set a = 0, i.e. the spheres are in equilibrium as they fall toward each other. I also see the assumption of equilibrium made in other solutions of this problem on the web. Why is this assumption justified?