Repulsion between two small spheres

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The discussion focuses on calculating the electric repulsion force between two small spheres, each with a deficit of 1.0 x 10^8 electrons, separated by 1.0 m. The relevant equations include the charge of an electron (1.602 x 10^-19 C) and the Coulomb's law formula for force. The calculated force of repulsion is confirmed to be 2.3 x 10^-12 N, aligning with the textbook answer. Participants clarify the use of constants and the proper application of formulas to arrive at the solution. The discussion emphasizes the importance of correctly applying physics principles to solve the problem.
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Homework Statement


Calculate the force of electric repulsion between two small spheres placed 1.0 m apart if each has a deficit of 1.0 x 10^8 electrons.

Homework Equations



N = q/e
qe = mg
q = mg / e
q = mgr / Vb
e = 1.602 x 10^-19 C.
k = 9 x 10^9 - not sure if relevant or not.
Fe = qe
Answer ( as stated in the textbook): 2.3 x 10^-12N

The Attempt at a Solution


Fe = qe?
r = 1. 0 m
e constant used
g = 9.8 N/kg?
Fe = (1.0 x 10^8 C)( 1.6 x 10^-19 C)x (1.0m/9.8N/kg) = 1.63 x 10^-12 N.
 
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Through my reasoning, I found the answer.


Charge of one electron = 1.602 x 10^-19 C
Charge of a sphere = 1.602 x 10^-19 x 1.0 x 10^8 C

F = (1/4piÈ) Q1Q2/d^2
(1/4piÈ) is a constant equal to 9 x 10^9
F = 9x10^9 x (1.602x10^-11) x (1.602x10^-11) / 1
F = 2.3 x 10^-12 N
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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