- #1
skanda9051
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Please some one help me how to solve this problem
integral-r^2 sin(theta) d(theta) d(phi)
integral-r^2 sin(theta) d(theta) d(phi)
Solve Surface Integral: r^2 sin(theta)
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Homework Help Overview
The discussion revolves around evaluating a surface integral involving the expression r^2 sin(theta) in the context of magnetic flux through a sphere of radius r. Participants are exploring the integration limits and the nature of the double integral in spherical coordinates.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants are questioning the integration limits for theta and phi in the context of spherical coordinates. There is a discussion about the nature of the integral and how to approach integrating the expression given.
Discussion Status
Some participants are providing guidance on the limits of integration in spherical coordinates, while others are seeking clarification on how to handle the double integral. There is an ongoing exploration of the problem without a clear consensus on the approach.
Contextual Notes
Participants note that the limits for theta and phi are defined by spherical coordinates, with phi running from 0 to 2pi and theta from 0 to pi. There is an emphasis on understanding the setup of the integral rather than solving it directly.
- #2
I like Serena
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MHB
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Hi skanda9051! 
What did you try?
That would help me to know what I should explain to you.
What did you try?
That would help me to know what I should explain to you.
- #3
skanda9051
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Well its magnetic flux E through a sphere of radius r and flux is given.
integral E. da=integral 1/4pi Eo (q/r^2).(r^2 sin(theta) d(theta) d(phi) they have given answer as q/Eo:-). My doubt is since it is surface integral there should be 2 limits one with respect to theta and another with respect to phi:-). So how did they integrate with respect to phi
integral E. da=integral 1/4pi Eo (q/r^2).(r^2 sin(theta) d(theta) d(phi) they have given answer as q/Eo:-). My doubt is since it is surface integral there should be 2 limits one with respect to theta and another with respect to phi:-). So how did they integrate with respect to phi
- #4
I like Serena
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MHB
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Yes, there are limits wrt theta and another wrt to phi.
This is be a double integral and not a single integral.
The limits are defined by the definition of spherical coordinates, although you do not need them to integrate your expression.
How would you integrate \int 5 d\phi?
And how would you integrate \int 5 \sin(\theta) d\theta?
Btw, in (these) spherical coordinates phi runs from 0 to 2pi, and theta runs from 0 to pi.
This is be a double integral and not a single integral.
The limits are defined by the definition of spherical coordinates, although you do not need them to integrate your expression.
How would you integrate \int 5 d\phi?
And how would you integrate \int 5 \sin(\theta) d\theta?
Btw, in (these) spherical coordinates phi runs from 0 to 2pi, and theta runs from 0 to pi.
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