Calculating Flux for Hemispheres of Different Radii

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SUMMARY

The discussion focuses on calculating the electric flux through three surfaces defined by two hemispherical surfaces of radii r1 and r2 centered around a point charge. The electric field is given by the equation \(\vec{E}(\vec{r}) = \frac{C}{r^2} \hat{r}\), where C is a constant proportional to the charge. The electric flux is determined by integrating the dot product of the electric field and the differential area element (dA) across the defined surfaces. Clarification is sought regarding the relationship between the provided images and the three surfaces involved in the calculation.

PREREQUISITES
  • Understanding of electric flux and its mathematical representation.
  • Familiarity with vector calculus, particularly dot products and integrals.
  • Knowledge of electric fields generated by point charges.
  • Basic concepts of geometry related to hemispherical surfaces.
NEXT STEPS
  • Study the concept of electric flux in detail, focusing on Gauss's Law.
  • Learn how to perform surface integrals in vector calculus.
  • Explore the relationship between electric fields and charge distributions.
  • Review examples of calculating electric flux through various geometries.
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone seeking to understand electric flux calculations involving point charges and hemispherical surfaces.

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Homework Statement



For some reason, I'm not quite understanding this scenario.

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32005.jpg


Two hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are centered at a point charge and are facing each other so that their edges define an annular ring (surface 3), as shown. The field at position \vec{r} due to the point charge is:

\vec{E}(\vec{r})= [C/(r^2)]*\hat{r}

where C is a constant proportional to the charge, r=|\vec{r}|, and \hat{r}=\vec{r}/r is the unit vector in the radial direction. "

I'm supposed to find electric flux through the three different surfaces, but for some reason, this picture just doesn't make sense to me.


Homework Equations



Electric flux is the integral of the dot product of electric field and dA (differential area element).



The Attempt at a Solution



I want to try figuring it out on my own first before I ask for help, but I don't quite understand this scenario. For example, I don't understand how the two images provided correlate, and I don't understand what the three different surfaces are. Sorry if the answer to this is obvious. ><
 
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You don't need to open it. It's just an image to help you understand the surfaces.
 

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