Sapling Learning There are two identical, positively charged conducting spheres

Question

Sapling Learning There are two identical, positively charged conducting spheres fixed in space. The spheres are 35.0 cm apart (center to center) and repel each other with an electrostatic force of F1 0.0750 N. Then, a thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed the spheres still repel but with a force of F2 0.100N. Using this information, findthe initial charge on each sphere, quand qz if initially q qz. The Coulomb Force constant is k 1/(4meo) 8.99 x10 N. m icz. Number Number O Previous Give Up s view solution heck Answer 0 Next Exit -l Hint

Explanation / Answer

F = kq1q2/r^2

initially

F1 = kq1q2/r^2

r = 35 cm = 0.35 m

F1 = 0.0750 N

q1q2 = F1*r^2/k

q1q2 = 1.02 x 10^-12

now after removing the thin wire both sphere have same amount of charge

F2 = kq1q2/r^2

F2 = 0.100 N

now q1 = q2 = q

q = 1.167 x 10^-6

q1+q2 = 2.235 x 10^-6

q2 = 2.235 x 10^-6 -q1

q1q2 = 1.02 x 10^-12

q1*(2.235 x 10^-6 -q1) = 1.02 x 10^-12

2.235 x 10^-6 q1 - q1^2 = 1.02 x 10^-12

q1^2 - 2.235 x 10^-6q1 + 1.02 x10^-12

solving this quadratic equation

q1 = 1.6 x 10^-6 C , 6.39 x 10^-7

q1< q2

q1 = 6.39 x 10^-7 C

q2 = 1.6 x 10^-6 C

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