Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F=x²yi + 3y³zj+3zk across the surface S: r(r,0) = r cos 0i+ r sin 0j +rk, 0≤r≤5, 0≤0 ≤2 in the direction with a positive k-component for n.The flux of the curl of the field F is(Type an exact answer, using as needed.)

Answered: Image /qna-images/answer/0a1b9524-d90d-4081-840d-3a998488f4e0.jpgSo, flux of curl F is .

Answered: Use the surface integral in Stokes'…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F = 3yi + (5 - 5x)j + (z² − 2)k S: r(0,0) = (√5 sin & cos 0) i + (√√5 sin þ sin 0)j + (√5 cos $) k, 0≤þ≤ñ/2, 0≤0≤2 The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is (Type an exact answer, using as needed.)
B2: Assume K is a body (Area) that is coherent. Let C be the curve that is parametised by the following equation (tan () .cos"(), sin°(1) ) osisa. Assume the following vector field thet is well defined in "K" and "a" is the value that gives Fa potential V(x, y, z). axz 1 + 2r, x²z+ y + 2y, + 2z 1²z + y° F(x, y, z) = 1²z + y_ a) Calculate a) b) Calculate the lineintegral F - dr.
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Let vector field F be given, C the curve with counterclockwise orientation looking from the direction of the positive z-axis. Calculate the line integral of the dot prpoduct F and dR.
Calculate the circulation of the field F around the closed curve C. Circulation means line integralF = - 6/7 x 2y i -6/7 xy 2 j; curve C is r(t) = 7 cos t i + 7 sin t j, 0 ≤ t ≤ 2π - 12 - 12/7 - 6 0
For the vector field G = (yey + 4 cos(4x + y))i + (xeªy + cos(4x + y)) ♬ find the line integral of G along the curve C from the origin along the x-axis to the point (4,0) and then counterclockwise around the circumference of the circle x² + y² = 16 to the point (4/√√2,4/√√2). ScĞ·dr = 0 }
(5xy, 5y?) for the region enclosed by the curves y = x? and y = x in the first quadrant, without parameterizing the curves (i.e. use the flux Compute the outward flux of the vector field F version of Green's theorem).
Prove Stokes theorem for the vector field P over the triangle area bounded by this path by the path indicated by the arrows in the xy planet in the figure.
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F = 4yi + (5-2x)j + (z² - 2)k S: r(0, 0) =(√6 sin cos 0) i + ( √5 sin ô sin 0)j + (√√6 cos ¢) k, 0≤ ≤r/2, 0≤0≤2r The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is (Type an exact answer, using as needed.)

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