Two identical conducting spheres, fixed in place, attract each other with an ele

Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.4466 N when separated by 50 cm, center-to-center. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0325 N. What were the initial charges on the spheres? Since one is negative and you cannot tell which is positive or negative, there are two solutions. Take the absolute value of the charges and enter the smaller value here.

Explanation / Answer

F = K*q1*q2/r^2 = -0.4466

Given that r = 50 cm = 0.5 m

then q1*q2 = -0.4466*0.5*0.5/(9*10^9) = -0.0124*10^-9 C^2

after connecting to the conducting wire .now new charges are

q1' = q2' = (q1+q2)/2

then q1'*q2' = (q1+q2)^2/4 = 0.0325*0.5*0.5/(9*10^9)

q1'*q2' = (q1+q2)^2/4 = 0.902*10^-12

q1+q2 = 1.899*10^-6 C

(q1-q2)^2 = (q1+q2)^2-4q1q2 = (0.003608*10^-9)+(4*0.0124*10^-9)

q1-q2 = 0.729*10^-5 = 7.290*10^-6

then q1 = 4.5945*10^-6 C

q2 = -2.6955*10^-6 C

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.