In the figure three identical conducting spheres form an equilateral triangle of

Question

In the figure three identical conducting spheres form an equilateral triangle of side length d = 19.2 cm. The sphere radii are much smaller than d and the sphere charges are qA = -3.42 nC, qB = -3.51 nC, and qC = +7.44 nC. (a) What is the magnitude of the electrostatic force between spheres A and C? The following steps are taken: A and B are connected by a thin wire and then disconnected; B is grounded by the wire, and the wire is then removed; B and C are connected by the wire and then disconnected. What now are the magnitudes of the electrostatic force (b) between spheres A and C and (c) between spheres B and C?

Explanation / Answer

a)

the magnitude of the electrostatic force between spheres A and C (Fac) = kqa*qb/a^2

Fac = 9*10^9*3.42*10^(-9)*3.51*10^(-9)/(0.192)^2 = 2.93*10^(-6) N

Connecting A and B equalizes the charges on the two:

qa2 = qb2 = (qa + qb)/2

Grounding B then drops the charge on B to 0:

qb3 = 0

Connecting B and C then equalizes the charge on them:

qb4 = qc4 = qc/2

so

(b) Fac = k(qa + qb)qc/(4*a^2)

Fac = 9*10^9*(3.42+3.51)*10^(-9)*7.44*10^(-9)/(4*0.192^2) = 3.15*10^(-6) N

(c) Fbc = (kqC^2)/4

Fbc = 9*10^9*7.44*10^(-9)*7.44*10^(-9)/(4*0.192^2) = 3.38*10^(-6) N

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