Week 8 Applications of Divergence Theorem and Line Integrals

Question 1

what does Divergence Theorem require

Answer 1

no “open” surface so must have a closed surface that encloses a volume

Question 2

what does the continuity equation do

Answer 2

expresses the fact that the quantity (q) is conserved

Question 3

what is the continuity equation

Answer 3

dρ/dt + ∇*J = 0

J is the flux of q

Question 4

what is the general line integral formula for a function f

Answer 4

∫ f dl

Question 5

what must be known in order to evaluate a line integral

Answer 5

the path

Question 6

what must happen for a line integral when evaluating a vector

Answer 6

the elemental must become a vector so that you are integrating a vector dot product

Question 7

what is the special line integral case

Answer 7

when integrating around a closed loop the line integral is called the circulation

Question 8

what are the three steps for evaluating a line integral

Answer 8

> Define dl in appropriate coord system
Take the dot product of the vector and dl
Use the equation of the curve to express this in terms of one integration variable