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 65.0 cm (this is the center-to-center distance), one ball exerts an attractive force of 2.30 N on the second ball. The balls are then touched together briefly (charge is conserved in this process), and then again separated by 65.0 cm. Now both balls have a positive charge, and the force that one ball exerts on the other is a repulsive force of 1.20 N. For this problem, use

and assume that the radius of each ball is small compared to 65.0 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!)

Please help!!! :(

Explanation / Answer

a)

let the charge on each after touching = q

r = distance between spheres = 0.65 m

F = force = 1.20

Force between the charges is given as

F = k q2/r2

1.20 = (9 x 109) q2 /0.652

q = 7.5 x 10-6 C

b)

let positive charge be "q1" and negative charge be "q2"

so q1 + q2 = 2q

q1 + q2 = 2 (7.5 x 10-6 )

q1 + q2 = 15 x 10-6                         eq-1

Force between charges is given as

F = k q1 q2/r2 = k q1 q2/0.652

2.3 = (9 x 109) q1 q2/0.652

q1 q2 = - 1.08 x 10-10    eq-2

using eq-1 and eq-2

q1 + (-1.08 x 10-10 /q1)= 15 x 10-6  

q1 = - 5.32 x 10-6

Positive charge = q2 = 15 x 10-6 - (- 5.32 x 10-6 ) = 20.32 x 10-6

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