Electric field at centre of a hollow hemisphere shell.

[uOEE]

Homework Statement

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.

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

 

[TSny]

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.

 

[uOEE]

How would I treat the vector? My apologies. Calculus is not my strong suit.

 

[uOEE]

How would I go about doing that? Calculus is not my stop suit. And also, thanks for the help.

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.

 

[TSny]

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.)

 

[isac learning]

 

[isac learning]