Displacement current inside capacitor

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The discussion centers on a discrepancy in the solution manual for a physics problem involving displacement current in a capacitor. The author of the manual calculates electric flux using the entire Amperian loop area, while the user argues that only the area of the capacitor plates should be considered, as the electric field outside is assumed to be zero. The derived expression for the magnetic field suggests that it increases with distance from the center of the capacitor plates, which the user finds counterintuitive. The user concludes that the magnetic field should only be evaluated within the radius of the capacitor plates, resolving their doubts about the solution. Overall, the user confirms their understanding of the problem and its solution.
issacnewton
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Hi

I have already solved the problem. I just have some doubts about the solution given in the
solution manual. This is "Physics for scientists and engineers" by Serway, Jewett
In the solution for part b) , the author has taken the area of whole Amperian loop while
calculating the electric flux through it. The book itself derives the expression for the displacement current taking only the area of the capacitor plates, which makes sense , since
its probably assumed that the electric field outside the volume between the plates is zero.
So ,in the solution of the problem, the author derives the expression for the magnetic field at a distance r from the center of the capacitor plates as

B=\frac {\mu_{o} I r}{2A}

it doesn't make sense that B increases as r, distance from the center of the capacitors,
increases.
 

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I think I got it, The r at which the author asks for the magnetic field is less than the radius
of the capacitor plates. So we have to consider the area of the amperian loop only.
So problem is solved.
 
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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