Two objects are identical and small enough that their sizes can beignored relati

Question

Two objects are identical and small enough that their sizes can beignored relative to the distance between them, which is 0.226 m. Ina vacuum, each object carries a different charge, and they attracteach other with a force of 1.60 N. The objects are brought intocontact, so the net charge is shared equally, and then they arereturned to their initial positions. Now it is found that theobjects repel one another with a force whose magnitude is equal tothat of the initial attractive force. What is the initial charge oneach object, the answer to part (a) being the onewith the greater (and positive) value?

Thanks so much!!!

Explanation / Answer

r = 0.226 m, F = 1.60 N before contact, charges are Q and -q (where Q > q > 0) F = kQq/r2 q = Fr2/(kQ) after contact, charge is (Q - q)/2 each, F = k(Q -q)2/(4r2 Qq = (Q - q)2/4 (Q - q)2 = 4Qq Q2 - 6Qq + q2 = 0 Q2 - 6Fr2/k +F2r4/(k2Q2) = 0 Q4 - 6Fr2/k * Q2 +F2r4/k2 = 0 Q2 = [6Fr2/k +(36F2r4/k2 -4F2r4/k2)]/2 = (3 +22)Fr2/k = 5.29*10-11 Q = 7.27*10-6 C

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