Given that F = ra,-xzay-ya, calculate the circulation of F around the (closed) path shown in...
Find the circulation and flux of the field F around and across the closed semicircular path that consists of the semicircular arch r(t)=(a cost)i +(a sint)j, Ostst, followed by the line segment rz(t)=ti, -ast sa F = x’i+y? j
One important quantity to characterise a fluid is the circulation Given Γ, a closed oriented path inside the fluid, the circulation C, along the path Γ is the integral a) Consider a cylindrical reservoir of radius r containing a fluid rotating with constant angular velocity ω. What is the circulation Cr with path defined as in figure ? Figure 1 b) Now, let us consider the case in which the velocity is not constant but rather the circulation, around any...
Find the circulation of F = xi +8zj + 3yk around the closed path consisting of the following three curves traversed in the direction of increasing t. (0,1,5 Cq:8/(t) = (cos t)i + (sin t)j + tk, Ostsa/2 Cz: r(t) = 1 + (1/2)(1 – t)k, Osts1 Cz. 13(t) = ti + (1 -t)j, Osts1 (1,0,0)
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. 11) F-3yi + yj + zk: C: the counterclockwise path around the boundary of the = 1
and ra E cm 44 Figure 29-68 shows two closed paths wrapped around two conduct- ing loops earrying currents i S.0 A and iy 3.0 A. What is the value of the integral f B-ds for (a) path 1 and (b) path 2? Figure 29-68 Problem 44 SSH Fach of tha eimbt
Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed curve C, where: (Sy 7sin() 5)
Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed curve C, where: (Sy 7sin() 5)
F=(-x-y)i+(x+y)j, curve C is the counterclockwise path around the circle with radius 2 centered at (8,8)math
Use Green's Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C. F(x, y) = (3x2+y)i + 3xy2jC: boundary of the region lying between the graphs of y = √x. y = 0, and x = 1
A vector field F is given as (a) Find 9 F dl around the closed triangular contour C shown in Figure 1-27 (b) Find (VxF) ds over the triangular surface (bounded by C) and verify Stokes' theorem (c) Can F be expressed as the gradient of a scalar? Explain why. -1 Figure 1-27.A triangular contour.
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper hemisphere x2 + y2 + z2 = 16 (z z 0) by the cylinder x2+ y2 =4 27)
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper...