Two small identical conducting balls start with different amounts of charge on t

Question

Two small identical conducting balls start with different amounts of charge on them. Initially, when they are separated by 60.0 cm (this is the center-to-center distance), one ball exerts an attractive force of 2.50 N on the second ball. The balls are then touched together briefly (charge is conserved in this process), and then again separated by 60.0 cm. Now both balls have a positive charge, and the force that one ball exerts on the other is a repulsive force of 1.10 N. For this problem, use k = 9.0 x 109 N m2 /cº, and assume that the radius of each ball is small compared to 60.0 cm. (a) After the two balls have been touched together, what is the charge on each ball? (b) Before they were touched together, one ball had a positive charge. How much charge did that ball have? (C) Before they were touched together, one ball had a negative charge. How much charge did that ball have? (Don't forget to include the minus sign!) Additional Materials O Section 16-3: Coulomb's Law O eBook

Explanation / Answer

total charge on them is +ve that means magnitude of positive charge is greater.

q1 -> magnitude of +ve charge

q2 -> magnitude of -ve charge

F = k q1 q2 / d^2

2.50 = (9 x 10^9)q1 q2 / 0.60^2

q1 q2 = 1 x 10^-10 ....... (i)

after they are touched and removed.

then q = (q1 - q2)/2

1.10 = k (q1 - q2)^2 / (4 x 0.60^2)

q1 - q2 = 13.3 x 10^-6 ..... (ii)

(q1 - q2)^2 + 4 q1 q2 = (q1 + q2)^2

q1 + q2 = 24 x 10^-6 ..... (iii)

adding both.

q1 = 18.6 x 10^-6 C

q2 = 5.35 x 10^-6 C

(A) q = (q1 - q2)/2 = 6.63 x 10^-6 C

(B) q1 = + 18.6 x 10^-6 C

(C) q2 = - 5.34 x 10^-6 C

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