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http://farside.ph.utexas.edu/teaching/em/lectures/node56.html

By equation 595, electric energy in the universe caused by an electric field is derived as http://farside.ph.utexas.edu/teaching/em/lectures/img1261.png. However, how come you can differentiate with respect to volume and say that the electric energy density is http://farside.ph.utexas.edu/teaching/em/lectures/img1262.png? After all, to come up with eq. 594, they had to make it a definite integral over all space so that the left term (in eq. 593) would converge to 0, and in order to do say the latter, wouldn't it have to be an indefinite integral?

Analogously, the integral from negative infinity to infinity of x/(x

-Jim

PS: sorry i don't know how to use LaTeX and this post is kind of unclear

By equation 595, electric energy in the universe caused by an electric field is derived as http://farside.ph.utexas.edu/teaching/em/lectures/img1261.png. However, how come you can differentiate with respect to volume and say that the electric energy density is http://farside.ph.utexas.edu/teaching/em/lectures/img1262.png? After all, to come up with eq. 594, they had to make it a definite integral over all space so that the left term (in eq. 593) would converge to 0, and in order to do say the latter, wouldn't it have to be an indefinite integral?

Analogously, the integral from negative infinity to infinity of x/(x

^{4}+ 1) is 0, but you cannot say that the function is equal to 0 for all x.-Jim

PS: sorry i don't know how to use LaTeX and this post is kind of unclear

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