Q3. Evaluate the circulation around the closed path shown in theFigure for, which represents a portion of a sphere, thevector field, B = 6rsinopf + 18rsin cosDa0.3.0.1O

The given closed path is shown: It is a part of the sphere with radius r=4. The curves enclose the…

Answered: Q3. Evaluate the circulation around the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Sketch a directional field for the equation. Identify at least 4 isoclines. dy dx = y + x Isoclines: Directional Field:
Consider the graph of an ellipse C, oriented counterclockwise. Graphs of the vector fields F,, F,, F, and F, along the curve C are given (see figures). Along C, F, and F, are tangent to C, and F, and F, are normal to C. Determine whether the following integrals are positive, negative, or equal to 0. b. F, · T ds JF T ds а. ·T ds с. C d. F -T ds F -n ds f. F,•n ds е. g. F•n ds h. Fn ds Vectors of F1 along C Vectors of F2 along C Vectors of F3 along C Vectors of F4 along C
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Show that if F = xi+yj + zk, then VXF=0. The curl of a vector field F = Mi+Nj + Pk is as follows. ap ƏN ?M ap dy dz dz ?x Use the formula above to find the curl of F=xi+yj + zk. curl F = VXF= VxF = V x (xi+yj+zk) dz dy = - i+ dy dz = i+ İ+ dx dz dz ?x + k j+ dy ax ?x ду ƏN ax k ƏM ду
For the vector field F and curve C, complete the following. a. Determine the points (if any) on the curve C at which the vector field F is tangent to C. b. Determine the points (if any) on the curve C at which the vector field F is normal to C. c. Sketch C and a few representative vectors of F on C. where C = = {(x,y): y - 3x² = -4} F= a. Where is F tangent to C? Select the correct choice below and fill in any answer boxes within your choice. OA. F is tangent to C at (Type an ordered pair. Use a comma to separate answers as needed.) OB. There are no points where F is tangent to C. OC. F is tangent to C at every point on C.
a) Calculate the flow of the vector field - F through the surface of a cylinder, see picture, with the radius r = 2 and the height h = 8. Use both possible calculation methods and explain the relationship. %3D 3z b) Explain Stokes' theorem and what to look for when using it.

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Q3. Evaluate the circulation around the closed path shown in the Figure for, which represents a portion of a sphere, the vector field, B = 6rsinof+ 18rsin cosp D 6.3 0.1 00