Electric Field due to a rod (1-dimensional)

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The discussion focuses on calculating the electric field at a specific point due to a charged rod. The individual expresses uncertainty about their choice of variables and the limits of integration in their solution. They seek feedback on their approach, indicating they are new to integrals and looking for guidance. There is a lack of responses, prompting them to consider sharing their solution for further assistance. Overall, the thread highlights the challenges faced by beginners in understanding electric fields and integration techniques.
thoff430
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Homework Statement



I am looking for the absolute value of the electric field at point A (see picture below) relative to the whole charged rod at the left side.

Homework Equations


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The Attempt at a Solution



I am not quite sure whether my choice for R and the boundaries of the integral are correct.
The solution seems to be legit at first sight, but as I'm just getting started with integrals, I would very thankful for any feedback or advice.

em1b-wc1-o4.JPG
 
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Well, no one? Do I need to type out my solution? Thought it was okay to scan it.
 
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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