Question

Two metal balls A and B of negligible radius, connected by a taut nonconducting thread of length 1.60 m, are floating at rest on Space Station Freedom between two metal bulkheads. Ball A carries charge q, and ball B carries charge 2q. Each ball is 1.06 m away from a bulkhead. (a) If the tension in the string is 3.50 N, what is the magnitude of q? (Ignore any contribution from induced charge in the bulkheads.) 22.32 Correct: Your answer is correct.

Answer 1

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 = kqq/r^2

in this case, substitute in the values given:

3.5 N = (9x10^9)(q)(2q)/(1.06)^2
3.5 = (9x10^9)(2q^2)/1.12
3.125 = (9x10^9)(2q^2)
0.1736x10^-9 = q^2
1.736x10^-10 = q^2
1.36x10^-5 = q

Therefore the charge on the first ball is is 1.36x10^-5 and the charge on the second ball is 2.72x10^-5