Electric field of half a spherical shell

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SUMMARY

The discussion focuses on calculating the electric field of a half spherical shell using Gauss's law. A user expresses difficulty in identifying an appropriate Gaussian surface for the problem. Another participant suggests an alternative approach by considering the symmetry of the system and integrating the contributions to the electric field from small segments of the circular intersection in the (x, y) plane, parametrized by angle φ. This method emphasizes the importance of symmetry in simplifying the calculations.

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  • Knowledge of integration techniques in calculus
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Homework Statement



Hey guys.
I've been trying to solve this question using Gauss law but I can't think of a surface that can contain this thing.
Is there another way to solve this?

Thanks a lot.


Homework Equations





The Attempt at a Solution

 

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Maybe it helps to draw a picture... suppose that the symmetry axis is the z-axis. Consider an intersection in the (x, y) plane, i.e. a circle of radius r(z) at height z. Draw some electric field lines to a point on the z-axis... the symmetry will provide some cancellations. If you use an angle [itex]\phi[/itex] to parametrize the circle, then you can divide the circle into small segments of length [itex]r(z) \, d\phi[/itex] and write down the contribution to the E-field from each segment. Once you have that, all you have to do is sum (i.e. integrate) over phi.

Yes I know, it's a lot of work :sad:
 

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