Two identical conducting spheres, fixed in place, attract eachother with an elec

Question

Two identical conducting spheres, fixed in place, attract eachother with an electrostatic force of 0.104 N when theircenter-to-center separation is 61.5 cm. The spheres are thenconnected by a thin conducting wire. When the wire is removed, thespheres repel each other with an electrostatic force of 0.0406 N.Of the initial charges on the spheres, with a positive net charge,what was (a) the negative charge in coulombs onone of them and (b) the positive charge incoulombs on the other?

(a)

Number

Units

(b)

Number

Units

(a)

Number

Units

C

Explanation / Answer

F1 = -K Q1 Q2 /R2 F2 = K (Q1 - q)(Q2 + q)/R2 F2 / F1 = [Q1Q2 +q (Q1 - Q2) - q2]/(Q1Q2) Get Q1 Q2 from the first equation as thenecessary values are given Also, Q1 - q = Q2 + q and(Q1 - Q2) = 2q   charges must beequal for equilibrium This is enough information to solve the quadratic in q Let F2 = K Q'2 / R2 and solvefor Q' Q' = Q1 - q = Q2 + q and solve forQ1 & Q2

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