Use Stokes' Theorem to compute the flux of the curl of the vector field F = (e² – y, x + e²", cos(xz)) across the upper hemisphere a? + y? + z2 = 1, z > 1 with outward normal.

Q: Find an equation of the plane through the origin such that the circulation of the field F = zi + xj…

A: Given the circulation of the field F = zi + xj + yk along the intersection of the planeand the…

Q: F= (y, 2x, -z) and C is the circle x² +y² = 9

A:

Q: Find the flux of the field F = 2xy i + 2yz j + 2xz k upward across the portion of the plane x + y +…

A:

Q: Use the surface integral in Stokes Theorem to calculate the flux of the curl of the field F = 5zi +…

A: Stoke' s theorem ∫CF.dr =∫∫scurl F .ds Given  F=5z , x , 2y  and r =r cosθ , r sinθ , 25-r2   ;…

Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: F =…

A:

Q: 4. Use Stoke's theorem to calculate the flux of the curl of the field F = (x – y)i + (y – z)j+ (z –…

A:

Q: Calculate the circulation of the field F = (2xy,y²) in a counterclockwise direction and the outward…

A: Consider the given field. F=2xy,y2 And, the given curves are defined as, y=x and y=x3 The green…

Q: · Verify Stokes's Theorem for the vector field F(x, y, z) = ( yz, – xz, z) over the cone z² = x² +…

A: Given problem is :

Q: Calculate the flux of the vector field F(x, y, z) = 5i + 2j+ zk through the closed circular cylinder…

A:

Q: Calculate the flux of the vector field V = 5i through a square of sides 4 m in the y-z plane (0 s ys…

A: Given V = 5i Area oriented towards positive x direction

Q: Find the outward flux of the field F = (x + y)î + yĵ + zk across the closed surface: S: z = 16x² -…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across…

A:

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

A:

Q: Find the flux of the vector field F (x, y, z) = (e-y, -y, x sin z) across the positively oriented…

A:

Q: ompute the flux of the vector field F = ri + yj+ zk through the surface S, which is a closed…

A:

Q: Use Stokes' theorem to find the circulation of the vector field F around any smooth, simple closed…

A: We will use basic knowledge of vector calculus, in particular the properties of Curl and gradient…

Q: Find the flux of the field F = xy i - z k outward (normal away from the z-axis) through the cone z =…

A:

Q: Use Stokes' Theorem to find the circulation of the vector field F = 2xzi + (3x + yz)j + x²k around…

A:

Q: 4. Compute the outward flux of the vector field F(r) = (r, y', =') through the unit sphere r² + y² +…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = +z)i+ (x…

A:

Q: Find the net flux of the vector field F(x, y, z) = (2x, - 2y, z) over the closed surface enclosed by…

A:

Q: use the surface integral in Stokes’ Theorem tocalculate the flux of the curl of the field F across…

A: Given  F=(y-z)i+(z-x)j+(x+z)k S:r(r,θ)=(rcosθ)i+(rsinθ)j+(9-r2)k 0≤r≤3, o≤θ≤2π

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

A: The given question can be solved as shown in step2

Q: Find the flux of the field F = x i + y j + z k across the sphere x2 + y2 + z2 = a2 in the direction…

A:

Q: Q1 Use Stokes theorem to compute the flux of the curl of a vector field F = (2x – y)ĩ – yz? j- y²zk…

A:

Q: Find the flux of the vector field F = (y, - a, z) through the helicoid with parameterization r(u, v)…

A:

Q: 4. Verify Stokes's Theorem for the vector field F(x, y, z) = ( yz, – xz, z) over the cone z² = x² +…

A: a) Given that the vector field Fx,y,z=yz,-xz,z over the cone  z2=x2+y2 with 0≤z≤2 oriented downward.…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= zi+…

A: Calculate the flux of the curl of the field F = z i + 5 x j + y k, by using the surface integral in…

Q: Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the…

A: Given surface 'S' is surrounding region D bounded by the planes y=0, z=0, z=2-y and z=1-x2

Q: (a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0 <y53…

A: If E be a  solid region bounded by surface of S with positive orientation then for a vector field…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across…

A:

Q: Compute the flux of the vector field F = xi + yj + zk through the surface S, which is a closed…

A:

Q: Find the outward flux of the field F = 6xyi + 4yzj + 2xzk across the surface of the cube cut from…

A:

Q: Compute the line integral of the vector field F=⟨6y,−6x⟩ over the circle x2+y2=1 oriented clockwise…

A: Given: F=6y dx - 6x dyand Let  x= cos t,   y= sin t    ⇒   dx = -sin…

Q: Verify Stokes’ Theorem for the vector field F = 2xyi + xj + ( y + z)k and surface z = 4 - x2 - y2,…

A:

Q: Compute the work done by the vector field F(x, y) = (ry, x² + y³) when moving a particle…

A:

Q: F =(-y,x,z) across the solid sphere E %3D

A: we have to find the outward flux

Q: - For the vector field in the xy plane: F= (zi - v)), use Stokes theorem to compute the line…

A: We will use stokes theorem for 2d

Q: 15. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y + z)k and the surface z = 4 – x²…

A: please comment if you need any clarification. If you find my answer useful put thumbs up. Thank you.

Q: Find the surface integral to evaluate the flux of the vector field F=, where S is the surface of the…

A:

Q: Find the outward flux of the field F = xz i + yz j + k across the surface of the upper cap cut from…

A:

Q: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 3yi +…

A: Given, F→=3yi^+5-3xj^+z2-2k^r→=3sinφcosθi^+3sinφsinθj^+3cosφk^ So, the flux of curl F is, Flux of…

Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (esin x + 2y², 6x + tan-…

A: We have to find the work done by the force field F→x,y,z=esinx+2y2,6x+tan-1y,xz in moving a particle…

Q: Find the outward flux of the field F = 2xy i + 2yz j + 2xz k across the surface of the cube cut from…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = (y +z)i+…

A:

Q: Compute the flux of the vector field F = 2xi + 2yj through the surface S, which is the part of the…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = by the…

A:

Q: Verify Stokes' Theorem holds for the vector field F = yz i + x k where S is the portion of the plane…

A: The given vector field is F=yzi^+xk^ where S is the portion of the plane 3x+2y+6z=6 in the first…

Q: 03 Verify Stokes theorem for the vector field F= 2(-+x)i-zyi-zy'k over the upper hlf surface of…

A: To find- Verify Stokes theorem for the vector field F→ = 2-y2 + xi→ + z2yj→ - zy2k→ over the upper…