Is the Potential of a Negatively Charged Conductor Always Negative?

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The potential of a negatively charged conductor is not necessarily negative, which can be confusing. While it may seem intuitive that a conductor with a negative charge would have a negative potential, the concept of electric potential is relative. The reference point for measuring potential is crucial, as it can be defined as zero at infinity or another location. This means that a negatively charged conductor can have a positive potential relative to a different point in space. Understanding the context of electric potential is essential for accurate interpretation.
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I was doing some T/F exercises and there was this one that had me confused:

The potential of a negatively charged conductor must be negative

Because it's conductor, i figured all of the conductor would be negatively charged and so it would have a negative potential, but apparently this statement is false. What am i missing?
Thanks
 
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Ahhh I get it now :P tricky setence tho, thanks!
 
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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