ucting spheres, fixed in place, attract each other with an electrostatic force o

Question

ucting spheres, fixed in place, attract each other with an electrostatic force of 0.129 N when their center-to-center ation is 62.8 cm. The wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0446 N. Of the spheres are then connected by a thin c nitial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.) Units Units

Explanation / Answer

let the initial charges be q1 and q2

q1 - q2 = q

r = distance between charges = 62.8 cm = 0.628 m

given that :

F = force between the charges = 0.129

k q1 q2/r2 = 0.129

(9 x 109) q1 q2 /(0.628)2 = 0.129

q1 q2 = 5.65 x 10-12  

q1 = (5.65 x 10-12 )/q2 eq-1

q = (q1 - q2)/2

given that :

k q2/r2 = 0.0446

(9 x 109) q2/(0.628)2 = 0.0446

q = 1.4 x 10-6

(q1 - q2)/2 = 1.4 x 10-6

q1 - q2 = 2.8 x 10-6

using eq-1

((5.65 x 10-12 )/q2 ) - q2 = 2.8 x 10-6

q2 = - 1.4 x 10-6

q1 = 4.2 x 10-6

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