Average circulation Let S be a small circular disk of radius Rcentered at the point P with a unit normal vector n. Let C be theboundary of S.a. Express the average circulation of the vector field F on S as asurface integral of ∇ x F.b. Argue that for small R, the average circulation approaches(∇ x F) | P ⋅ n (the component of ∇ x F in the direction of nevaluated at P) with the approximation improving as R → 0.

Q: 1/2 5) Consider vector field F(x, y,z) = ( 2/yz – 2xz', - 2x²z) for 1/2 x>0, y > 0 and z>0 a)…

A:

Q: Given the vector field F(x,y,z)= , find the divergence and the curl of F. I

A:

Q: A pasticle depicts ts motion in Such a ulay at time ť is P=xîty where, 2= acoskt and y=bsinkt. that…

A:

Q: Let the vector field F be given by F(x,y,z)=(y,xz,=z^2).  Evaluate its integral along the curve C…

A:

Q: The velocity field for a fluid is given by V=(X2t3)i+(2XYT)j. The convective acceleration in the…

A: Given, V=x2t3i^+2xytj^ Here, u=x2t3 and v=2xyt Convective acceleration in y-direction is given by:…

Q: Use Stokes' Theorem to find the circulation of F = 4yi +7zj +3ck around the triangle C' obtained by…

A:

Q: A vector is said to be conservative when it's: curl equal to zero Laplacian equal to zero divergence…

A: We know that ,  A conservative vector field , is a vector field  F  whose line integral  ∫C F·ds…

Q: Select all of the following curves Cand vector fields F for which Green's Theorem could be used to…

A: The chosen pairs were correct but you failed to include the first option. The correct answers are…

Q: Consider the vector field: F(x, y, z) Show that F is not Conservative, i.e., not a gradient. sin…

A:

Q: 4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in…

A:

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: r(t) = sin(t)i + cos(t)j + ek

A: We have to solve given problem:

Q: Verify Stokes' Theorem, given a vector field F, for the surface z=1-x², 0≤x≤ 1,0 ≤ y ≤ 2 There are…

A:

Q: Let vector field F=(xz,-y,z) and surface, S is a cylinder x² + y² = 4 for 3≤z≤0 with the outward…

A: According to Stoke's theorem If S is a smooth surface  bounded by a closed, smooth boundary curve C…

Q: Is the following vector-valued function continuous at t=0

A:

Q: Q1: Consider an electromagnetic (EM) in free space whose electric field is given by E = 60 exp [-i…

A:

Q: What is the relationship between the curvature tensor and the Riemann curvature tensor in…

A: The Riemann curvature tensor and the curvature tensor are essentially the same thing in the context…

Q: Let divF(x, y, z) = 4x³ + 4y3 +4z³, where F represents the flow of a vector field. Estimate the flux…

A: Given divF→x,y,z=4x3+4y3+4z3radius r=0.1 Centered at point 1,1,1

Q: down 2. 2)

A: Consider the given figure. Given a quarter cylinder of radius 2 and height 5 exists as shown in the…

Q: Define divergence of a velocity vector in a flow field. Highlight its physical significance.

A: The objective is to be to define and explain the physical significance of the divergence of a…

Q: (a) the unit vector in the same direction as à = (1,2,2) (b) the gradient of h at P (c) the…

A:

Q: A field is given as G = [25/(x² + y²)](xax + yay). Find (a) a unit vector in the direction of G at…

A: Vector field and vector

Q: to the graph of the vector-valued function r(t)= at t=1. find: A ) The unit tangent is B) The unit…

A: