Limits of Theta and Phi in Surface Integrals on a Sphere

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SUMMARY

The limits of theta and phi in surface integrals on a sphere are definitively established as follows: theta varies from 0 to 2π, while phi ranges from 0 to π when using standard mathematical notation. In contrast, engineering notation reverses these limits, with theta measuring co-latitude and phi measuring longitude. Understanding these limits is crucial for accurately performing surface integrals on spherical coordinates.

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sunny11119
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I am having problems in finding the limits in surface integral.. for example in case of sphere what will be the limits of theta and phi. somebody please answer quickly. Thanks
 
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Welcome to PF!

sunny11119 said:
I am having problems in finding the limits in surface integral.. for example in case of sphere what will be the limits of theta and phi. somebody please answer quickly. Thanks

Hi sunny11119! Welcome to PF! :smile:

theta goes from 0 to π, and phi from 0 to 2π

(or you can do it the other way round :wink:)
 
If you are using the standard mathematics notation, where [itex]\theta[/itex] measures "longitude" and [itex]\phi[/itex] measure "co-latitude", then to cover the entires sphere [itex]\theta[/itex] varies from 0 to [itex]2\pi[/itex] and [itex]\phi[/itex] from 0 to [itex]\pi[/itex]. "Engineering notation" reverses [itex]\theta[/itex] and [itex]\phi[/itex]. Of course, if you want to cover only a part of a spherical surface, that's another matter.
 

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