By Richard P. Feynman

undying and collectible, the lectures are crucial analyzing, not only for college kids of physics yet for somebody looking an advent to the sector from the inimitable Feynman.

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**Additional info for The Feynman Lectures on Physics, Vol. II: The New Millennium Edition: Mainly Electromagnetism and Matter**

**Example text**

So for any way of dividing the original volume, it must be generally true that the flux through the outer surface, which is the original integral, is equal to a sum of the fluxes out of all the little interior pieces. 4 (x, y + ∆y , z) 5 ∆y C C Cx 1 n 2 (x, y , z) 3-3 The flux from a cube; Gauss’ theorem We now take the special case of a small cube* and find an interesting formula for the flux out of it. Consider a cube whose edges are lined up with the axes as in Fig. 3-5. Let us suppose that the coordinates of the corner nearest the origin are x, y, z.

The simplest possible physical field is a scalar field. By a field, you remember, we mean a quantity which depends upon position in space. By a scalar field we merely mean a field which is characterized at each point by a single number—a scalar. Of course the number may change in time, but we need not worry about that for the moment. We will talk about what the field looks like at a given instant. As an example of a scalar field, consider a solid block of material which has been heated at some places and cooled at others, so that the temperature of the body varies from point to point in a complicated way.

The heat flow through ∆a2 is the same as through ∆a1 . If we choose some convenient set of axes, we could write T1 = T (x, y, z) and T2 = T (x + ∆x, y + ∆y, z + ∆z), where ∆x, ∆y, and ∆z are the components of the vector ∆R (Fig. 2-5). Remembering Eq. 7), we can write ∂T ∂T ∂T ∆T = ∆x + ∆y + ∆z. ∂x ∂y ∂z ∆z P2 ∆R ∆y P1 ∆x are also the x-, y-, and z-components of a vector. We write this new vector with the symbol ∇T . The symbol ∇ (called “del”) is an upside-down ∆, and is supposed to remind us of differentiation.