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Vector Calculus Question about Surface Integrals 
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#1
Dec412, 01:33 PM

P: 2

Why is it that when the force field is z^2 and you take the surface integral over a sphere of radius a using spherical coordinates, that yields the flux to be (4pi a^3 )/ 3
BUT in a calculus book, the force field is z instead of z^2 evaluated using polar coordinates and it yields the same amount of flux, (4pi a^3 )/ 3. How can this be when the force is different (z^2 instead of z?) Isn't it when you for example, get five times the force, like 5z you would get the answer multiplied by a factor of 5. When you square z it should come out to be different shouldn't it? Any help greatly appreciated. Thanks in advance 


#2
Dec412, 01:45 PM

P: 2

Please note that this is not a homework question. Simply a question that if you change the value of the force in your surface integral in this case, shouldn't the answer be different?



#3
Dec412, 02:23 PM

P: 350

Sorry I don't understand the question. What exactly is the integral being calculated? Alternatively, what exactly is the physical quantity being calculated? If it is the flux of a force field across the sphere, then what is the force field? You need to say what direction it is pointing.



#4
Dec512, 08:23 AM

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Vector Calculus Question about Surface Integrals



#5
Dec1012, 11:27 PM

P: 428




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