Posted before and got the wrong answer, please help! In the figure three identic

Question

Posted before and got the wrong answer, please help!

In the figure three identical conducting spheres form an equilateral triangle of side length d- 20.8 cm. The sphere radii are much smaller than d and the sphere charges are qA --1.35 nC, qs 5.80 nC, and qc = +8.47 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

Apply Columb law of force to solve the problem

The electric force between the spheres A and C is

F_AC = kq_A q_C/ d^2 = 9 * 10^9 (1.35* 10^-9) (8.47 * 10^-9)/(0.208)^2 = 2.378 * 10^-6 N

(b)

after making contact with each other both A and B have charge of

q_A+ q_B/2 = ( -1.35 nC+(-5.8 nC)/2 = -3.575 nC

When B is grounded its charge is zero. After making contact with C, which has a charge
of B aquires a charge ( 0 +(-8.47 nC)/2 = -4.235 nC

q_A = -3.575 nC and q_B = q_C = -4.235 nC

F_AC = kq_Aq_C/d^2

= 9 * 10^9 ( -3.575 nC) ( -4.235 nC)/ ( 0.208)^2 = 3.149 * 10^-6 N

(c)

F_BC = kq_Bq_C/d^2

= 9 * 10^9 ( -4.235 nC) ( -4.235 nC)/ ( 0.208)^2 = 3.730 * 10^-6 N

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