I've been reading the text: Electricity and Magnetism, by Purcell.(adsbygoogle = window.adsbygoogle || []).push({});

I understand about the integral forms describing the electric field, but when trying to answer questions at the end of the chapter on Gauss's and Stokes's therorems I have not been able two. These two theorems supposedly transform the integral equations that describe an electric field into differential equations, yet there are still integrals in the equations:

Gauss:

[tex]Integrate[F*da,over surface]=Integrate[div F*dv,over volume][/tex]

[tex]div F=4\pi\rho, del^2*potential=-4\pi\rho[/tex]

Stokes:

[tex]Integrate[F*ds,over circ.]=Integrate[curl F*da,over surface][/tex]

[tex]del X A[/tex]

Questions:

1. I'm having trouble with looking at field lines and judging if div F=0 (or not zero) or curl F=0 (or not zero)

2. How to calculate flux/volume for Gauss problems. I see in the book they use the midpoint. Or flux/area for Stokes problems. Why do the choose the midpoint?

3. Also would someone explain the sidways derivative of the curl, I don't understand why it is the way it is.

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# Gauss's Divergance Theorem and Stokes's Theorem

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