Consider two metal spheres of radii

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The discussion centers on calculating the ratio of surface charge densities for two metal spheres with different radii, both charged to the same potential. The initial attempt incorrectly assumes equal charge, leading to a miscalculation of the ratio. The correct approach recognizes that the spheres have different surface areas due to their sizes, affecting the charge distribution. The expected answer for the ratio of surface charge densities is 2, highlighting the importance of understanding the relationship between potential and charge density. Clarification on the distinction between potential and charge is crucial for solving the problem accurately.
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Homework Statement


Consider two metal spheres of radii r1 = R and r2 = 2R, both charged to the same potential V0.
a) What is the ratio n1/n2 of their surface charge densities?

Homework Equations


n(eta) = charge/area
Er = -dV/dr

The Attempt at a Solution


a) n1/n2 = Q/(4*pi*R2) / Q/(16*pi*R2) = 4

The answer is supposed to be 2, and I don't know what I'm doing wrong.
 
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The spheres are charged to the same potential (volts), not the same charge (Coulombs).
 

Thread 'Magnitude of buoyant force in fluids of different densities'

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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