Two metal balls A and B of negligible radius are floating at rest on Space Stati

Question

Two metal balls A and B of negligible radius are floating at rest on Space Station Freedom between two metal bulkheads, connected by a taut nonconducting thread of length2.45 m. Ball A carries charge q, and ball B carries charge 2q. Each ball is 1.12 m away from a bulkhead.

(a) If the tension in the string is 2.10 N, what is the magnitude of q? (Ignore any contribution from induced charge in the bulkheads.)
_____ C

(b) What happens to the system as time passes? Explain. (Assume the thread is oriented perpendicular to the bulkheads.)

Explanation / Answer

A. The tension within the string is the same as the force felt between the two objects. The force felt between two point objects due to there electrostatic repulsion is given by:
F = kq1*q2/r^2
in this case, substitute in the values given:

2.1 N = (9*10^9)(q)(2q)/2.45^2
2.1 = (9*10^9)(2q^2)/6.0025

q = (2.1*6.0025/(18*10^9))^0.5 = 2.64*10^-5 C
B. The system drifts towards the bulkhead nearest the 2q charge. This is because it induces a opposite charge in that portion of the bulkhead

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