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Chapter 14: Q 5. (page 1149)

Make a chart of all the new notation, definitions, and theorems in this section, including what each new item means in terms you already understand.

Short Answer

Expert verified

Notations, definitions and theorems are:

  • Divergence Theorem
  • W
  • 蔚0
  • 蚁(x)
  • 惟
  • Gauss's Law
  • Integral Form of Gauss's Law

Step by step solution

01

Given Information

We need to make chart of all new notations, definitions, theorems in section.

02

Explanation

NotationMeaning, Definition and Theorem
Divergence TheoremLet F(x,y,z)be defined on open interval containingW, then
鈭�SF(x,y,z)路ndS=鈭�WdivF(x,y,z)dVn is unit normal vector.

W		Region inR3whose boundary is smooth or piecewise smooth closed oriented surface.

蔚0		Permittivity of Free Space

蚁(x)		Charge Density
惟
Region enclosed by surface
Gauss's Law鈭�路E(x)=蚁(x)蔚0
Integral form of Gauss's Law鈭�SdivEdA=1蔚0鈭�惟蚁dV

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Most popular questions from this chapter

If the velocity of a flow of a gas at a point (x, y, z) is represented by F and the gas is expanding at that point, what does this imply about the divergence of F at the point?

Why is the orientation of S important to the statement of

Stokes鈥� Theorem? What will change if the orientation is

reversed?

Integrate the given function over the accompanying surface in Exercises 27鈥�34.
f(x,y,z)=x2-y+3z, where Sis the portion of the plane with equation 2x-6y+3z=1whose preimage in the xz plane is the region bounded by the coordinate axes and the lines with equations z = 4 and x = z.

ComputethedivergenceofthevectorfieldsinExercises17鈥�22.G(x,y,z)=yz2i鈭�xsinzj+x2exyk

F(x,y,z)=5i+13j+2k, where S is the unit sphere, with n pointing outwards.
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