Two objects are identical and small enough that their sizes can be ignored relat

Question

Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.238 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 1.11 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object, the answer to part (a) being the one with the greater (and positive) value?

Explanation / Answer

a)

Force between the charges :

F = k*q1*q2/r^2

= 9*10^9*q1*q2/0.238^2 = 1.11

So, q1*q2 = 6.99*10^-12 C^2 --------------- (1)

When charges are shared equally, charge on each charge = (q1-q2)/2

So, force now between them = k*((q1-q2)/2)^2/0.238^2 = 1.11

So, 9*10^9*((q1-q2)/2)^2/0.238^2 = 1.11

So, q1 - q2 = 5.29*10^-6 C --------- (2)

So, solving both equations we get :

q1 = 6.38*10^-6 C <------ answer

q2 = -1.09*10^-6 C <--------- answer

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