I have tried the following, but it was incorrect and would greatly appreciate as

Question

I have tried the following, but it was incorrect and would greatly appreciate assistance in helping me figure out what I'm doing wrong and how to correctly solve this problem:

A)

q1 + q2 = 7.5 mC.

q2 = (31 cm)/(21.5 cm)(q1)

q2 = 1.441860465(q1)

(q1) + 1.441860465(q1) = 7.5 mC

2.441860465 (q1) = 7.5 mC

q1 = 3.071428572 mC => Charge on Sphere A (was incorrect)

q2 = 7.5 mC - 3.071428572 mC = 4.4285714 mC

B)

Tension = Electric Force = (k)(q1)(q2)/(d2) = (8.99 x 109)(3.071428572 x 10-3)(4.4285714 x 10-3)/(0.8892) = 154724.9156 N (was also incorrect)

A total charge of 7.5 mC is shared by two metallic spheres A and B of radii 21.5 cm and 31 cm that are connected by a long thin wire of of length 0.735 m. Find the charge on sphere A

Explanation / Answer

A and B are connectd with a wire and hence both will have the same potential.

let Qa and Qb are the charges on each sphere

Pot of A = k Qa/Ra

Pot of B = kQb/Rb

Qa /Qb = Ra/Rb = 21.5/31 = 0.69

Qa + Qb = 7.5 mC , total charge

putting Qa = 0.69 Qb

Qb = 7.5/1.69 = 4.44 mC

Qa = 7.5 - 4.44 = 3.06 mC

distance between the charges d= 0.735 + 0.215 +0.31 = 1.26 m

Force F = 9.0E+9 * 4.44E-3 * 3.06E-3 /1.262 = 77.02 E+3 N

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