Electric field at centre of a hollow hemisphere shell.

AI Thread Summary
The discussion focuses on calculating the electric field at the center of a hollow hemisphere shell using spherical coordinates and differential elements. The original poster is struggling with their solution, suspecting a small mathematical error after multiple attempts. A key point raised is the incorrect treatment of the unit vector ##\hat{r}## as a constant during integration, which affects the outcome. Participants suggest using symmetry to determine the direction of the net electric field and to project the integrand accordingly. Clarifying these concepts is essential for accurately solving the problem.
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Homework Statement


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Homework Equations


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The Attempt at a Solution



Please excuse the poor writing. I believe it should be legible enough, but if you have any questions, i'll clarify or rewrite it.

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Please excuse the poor writing. I believe it should be legible enough, but if you have any questions, i'll clarify or rewrite it.

My steps for solving this was filling in the values into the formula given. Using a square differential element on the surface of the sphere, as well as spherical co-ordinates.

i'm sure i just have a small error somewhere in the math, but I'm not too sure where... I've redone the question 3 times.

These two sources, among others, show that my answer is wrong. Though I did my question differently, so i can't be sure where i went wrong.



http://www.personal.utulsa.edu/~alexei-grigoriev/index_files/Homework2_solutions.pdf
 
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Welcome to PF!

Looks like you treated the unit vector ##\hat{r}## as a constant vector when you pulled it out of the double integral. Does the direction of ##\hat{r}## vary as you integrate over the surface? If so, you cannot treat it as a constant vector.
 
How would I treat the vector? My apologies. Calculus is not my strong suit.
 
How would I go about doing that? Calculus is not my stop suit. And also, thanks for the help.
TSny said:
Welcome to PF!

Looks like you treated the unit vector ##\hat{r}## as a constant vector when you pulled it out of the double integral. Does the direction of ##\hat{r}## vary as you integrate over the surface? If so, you cannot treat it as a constant vector.
 
Use symmetry to see which direction the net E field will point. Then just work with the component of E that is in that direction. (Project your integrand into that direction.)
 
 
 
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