There are two identical, positively charged conducting spheres fixed in space. T

Question

There are two identical, positively charged conducting spheres fixed in space. The spheres .... (need both parts)

There are two identical, positively charged conducting spheres fixed in space. The spheres are 38.6 cm apart (center to center) and repel each other with an electrostatic force of F_1 = 0.0645 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 F_2 = 0.115 N. Using this information, find the initial charge on each sphere, q_1 and q_2 if initially q_1

Explanation / Answer

F1 = k*q1*q2/r^2 = 0.0645 N

q1*q2 = (0.0645*0.386^2)/(8.99*10^9)

q1*q2 = 1.06*10^-12

F2 = k*((q1+q2)/2)^2/r^2 = 0.115

(q1+q2)^2 = (0.115*0.386^2*4)/(8.99*10^9)

q1+q2 = 2.76*10^-6

(q1-q2)^2 = (q1+q2)^2-(4*q1*q2) = (7.62*10^-12)-(4*1.06*10^-12)

q1-q2 = 1.83*10^-6

----------------------------------

2*q1 = 4.59*10^-6

q1 = 2.295*10^-6 C

q2 = q1-(1.83*10^-6) = (2.295-1.83)*10^-6 = 0.465*10^-6 C

since q1 < q2

q1 = 0.465*10^-6 C

q2 = 2.295*10^-6 C

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