Im having a bit of a problem understanding the crucial part of the divergence theorem from Electromagnetic Fields and Waves by Lorrain and Corson. Ill try descibe the set up of the problem 1st and see if anyone can help me in any way before i continue with the electromagnetism course im doing as i want to be comfortable with the vector algebra.(adsbygoogle = window.adsbygoogle || []).push({});

The book considers the outward flux through a closed surface, in this case an infinitessimal volume dx dy dz and a vectorBwhose components Bx, By, Bz are functions of x,y,z. The value of Bx at the centre of the right-hand face may be taken to ve the average value over that face. Through the right-hand face of the volume element, the outgoing flux is

dΦR = (Bx + (dBx/dx)*(dx/2))dydz

This is the bit im puzzled at, i understand dydz is the area element and why its the x-component of the vector we use in the line integral but im not getting where the "+ (dBx/dx)*(dx/2)" is coming into the scene. Any suggestions?

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# Homework Help: Divergence Theorem Proof

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