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The book considers the outward flux through a closed surface, in this case an infinitessimal volume dx dy dz and a vector

**B**whose 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?

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?