A pair of Aluminum (Al) spheres are hanging by insulating threads, each with ove

Question

A pair of Aluminum (Al) spheres are hanging by insulating threads, each with overall length, L = 80 cm. The mass of each Al sphere is 25.0 grams. Given are the atomic weight of Al = 26.982 g/mole, and the atomic number, Z, for Al is Z(Al) = 13. Calculate the magnitude of the charge that must be present on each Al sphere, in order for the repulsive Coulomb force to cause the spheres to be separated by d = 1 mm; when each are hanging vertically from the 80 cm long threads, under the force of gravity?  

a) 1.84 x 10^-6 C; b) 1.6 x 10^-10 C; c) 26 x 10^-9 C; or d) 0.75 x 10^-3 C.

From the charge determined, calculate how many electrons (or protons), this corresponds to?

a) q = 26.3 x 10^6 electrons; b) q = 8 x 10^11 electrons; c) q = 13 x 10^14 electrons; or d) q = 11.5 x 10^12 electrons.

Please give solutions. Thank you.

Explanation / Answer

Here, tan(theta) = qE/mg

=>   tan(0.0358) = F/(0.025 * 9.8)

=> F =   1.531 * 10-4 N

Thus,   1.531 * 10-4   = 8.98 * 109 * q2/(10-3)2

=> q = 1.305 x 10-10 C

=> no of electrons = (1.305 x 10-10)/(1.6 * 10-19)

                               = 8.156 * 108

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