Question

(1 point) Use Stokes' Theorem to find the circulation of the vector field \( \vec{F} = 4xz \hat{i} + (x + 7yz) \hat{j} + x^2 \hat{k} \) around the circle \( x^2 + y^2 = 1, z = 5 \), oriented counterclockwise when viewed from above. circulation =

          (1 point) Use Stokes' Theorem to find the circulation of the vector field \( \vec{F} = 4xz \hat{i} + (x + 7yz) \hat{j} + x^2 \hat{k} \) around the circle \( x^2 + y^2 = 1, z = 5 \), oriented counterclockwise when viewed from above.

circulation =

(1 point) Use Stokes' Theorem to find the circulation of the vector field F⃗ = 4xz î + (x + 7yz) ĵ + x^2 k̂ around the circle x^2 + y^2 = 1, z = 5, oriented counterclockwise when viewed from above.

circulation =

Added by Danielle M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/11/2023

Step 1

The curl of F is given by the determinant of the following matrix: curl(F) = | i j k | | ∂/∂x ∂/∂y ∂/∂z | | 4xz x+7yz x^2 | Taking the partial derivatives, we get: ∂/∂x = 0 ∂/∂y = 7z ∂/∂z = 4x + 7y So the curl of F is: curl(F) = (7z - (4x + 7y))i - 0j Show more…

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(1 point) Use Stokes' Theorem to find the circulation of the vector field vec(F)=4xzvec(i)+(x+7yz)vec(j)+x^(2)vec(k) around the circle x^(2)+y^(2)=1,z=5, oriented counterclockwise when viewed from above. circulation = 1 point) Use Stokes' Theorem to find the circulation of the vector field F=4zi+(+7yz)j+2 around the circle2 u21.5,oriented counterclockwise when viewed from above circulation=