a charged object having 25 microcoulombs on it breaks into two pieces. if the force of repulsion between the two pieces i 1000Newtons when the pieces are 3cm apart, what is the charge on each piece? assume pieces act as a point charges
E = F/qtest = k(qa)/r^2 where F is the attractive/repulsive force
F = k(qa)(qb)/r^2 where k is 9*10^9, qa is charge of one piece, qb is charge of other piece, r is the radius between pieces
The Attempt at a Solution
firstly, do i assume the parts broken into are the same size/charge as each other? i don't think so, correct?
basically i used the second eq and set F = 1000, r = 0.03m, k = 9*10^9 and solved for qa in terms of qb
i then used the first eq and subbed in F =1000, qtest = 25*10^-6 coulombs and set that equal to kqa/r^2, where i subbed in what i got from the second eq in for qa and solved for qb
i got 2.5*ac^-5 coulombs for qb, i used qb in the second eq and got a qa of 4*10^-6
i know i did something wrong because when i sum the charges of each piece, qa and qb, i get less than the entire charge value given (25 microcoulombs). i get a sum of 2.9*10^-5 coulombs
is my approach even close, help appreciated...