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We were given an electric field defined by [itex]Kr^3[/itex], and asked to calculate what the total flux would be given a sphere of a radius R. I had already calculated the divergence of E to be equal to [itex]5kr^2[/itex]. So the first integral is calculating what the divergence over the area of the sphere is equal to, and our second integral is calculating what the surface integral of E * da is. By divergence theorem they should be equal but for me they are off by a factor of two.
[itex]\int_{\vartheta=0}^{2\pi} \int_{<br /> \varphi=0}^{\pi/2}\int_{\rho=0}^{R} 5Kr^2 (r^2 sin(\phi) d\rho d\phi d\theta[/itex]
which will then yield [itex]2K\pi R^5[/itex]
Here is the surface integral.
[itex]\oint\oint E * da[/itex]
where da will yield (4\pi R^2)
multiplying this times KR^3 gives us [itex]4K\pi R^5[/itex]
Any help on what to do here will be greatly appreciated.
THank you
[itex]\int_{\vartheta=0}^{2\pi} \int_{<br /> \varphi=0}^{\pi/2}\int_{\rho=0}^{R} 5Kr^2 (r^2 sin(\phi) d\rho d\phi d\theta[/itex]
which will then yield [itex]2K\pi R^5[/itex]
Here is the surface integral.
[itex]\oint\oint E * da[/itex]
where da will yield (4\pi R^2)
multiplying this times KR^3 gives us [itex]4K\pi R^5[/itex]
Any help on what to do here will be greatly appreciated.
THank you