Linear Charge Density (Question on the problem)

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The problem involves calculating the linear charge density of a circular arc with a total charge of -310e distributed along it. The charge converts to approximately -4.96E-17 C. The arc subtends an angle of 43°, which means it represents 43/360 of a full circle. To find the length of the arc, the radius and the angle in radians can be used. Understanding the subtended angle is crucial for solving the problem accurately.
exitwound
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Homework Statement



A charge of -310e is uniformly distributed along a circular arc of radius 4.15 cm, which subtends an angle of 43°. What is the linear charge density along the arc in C/m?

Homework Equations



Density = Charge/length

The Attempt at a Solution



Charge = -310(1.6E-19) = -4.96E-17 C

Length = ??

This is because I don't know what "subtends an angle of 43" means. Does it mean the circular arc is 43/360 degrees of a circle?
 
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exitwound said:
This is because I don't know what "subtends an angle of 43" means. Does it mean the circular arc is 43/360 degrees of a circle?
Yes, that's exactly what it means.
 
Okay, 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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