Question

Use Stokes' Theorem to compute the counterclockwise circulation of the vector field $\mathbf{F} = \langle 4y, 1z, 4x \rangle$ along the curve $C$, where $C$ is the rectangle with vertices $(0, 0, 3)$, $(2, 0, 3)$, $(2, 5, 3)$, and $(0, 5, 3)$. To apply Stokes' Theorem, you must first find the curl of the vector field. $\text{curl}(\mathbf{F}) = \square$ Now, use the curl to compute the circulation. $\text{Circulation} = \oint_C \mathbf{F} \cdot d\mathbf{r} = \square$

Name: use stokes theorem to compute the counterclockwise circulation of the vector field mathbff langle 4y 1z 4x rangle along the curve c where c is the rectangle with vertices 0 0 3 2 0 3 2 5 3 a 57038
Uploaded: 2023-11-29T15:46:59-08:00
Duration: 2 min 45 s
Channel: Zack A
Description: use stokes theorem to compute the counterclockwise circulation of the vector field mathbff langle 4y 1z 4x rangle along the curve c where c is the rectangle with vertices 0 0 3 2 0 3 2 5 3 a 57038

          Use Stokes' Theorem to compute the counterclockwise circulation of the vector field $\mathbf{F} = \langle 4y, 1z, 4x \rangle$ along the curve $C$, where $C$ is the rectangle with vertices $(0, 0, 3)$, $(2, 0, 3)$, $(2, 5, 3)$, and $(0, 5, 3)$.

To apply Stokes' Theorem, you must first find the curl of the vector field.

$\text{curl}(\mathbf{F}) = \square$

Now, use the curl to compute the circulation.

$\text{Circulation} = \oint_C \mathbf{F} \cdot d\mathbf{r} = \square$

use stokes theorem to compute the counterclockwise circulation of the vector field mathbff langle 4y 1z 4x rangle along the curve c where c is the rectangle with vertices 0 0 3 2 0 3 2 5 3 a 57038

Added by Matthew C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zack A

11/29/2023

Step 1

Let $\mathbf{F} = \langle P, Q, R \rangle$, where $P = 4y$, $Q = 1z$, and $R = 4x$. The curl of $\mathbf{F}$ is given by: $\text{curl}(\mathbf{F}) = \nabla \times \mathbf{F} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial}{\partial x} & Show more…

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Use Stokes' Theorem to compute the counterclockwise circulation of the vector field $\mathbf{F} = \langle 4y, 1z, 4x \rangle$ along the curve $C$, where $C$ is the rectangle with vertices $(0, 0, 3)$, $(2, 0, 3)$, $(2, 5, 3)$, and $(0, 5, 3)$. To apply Stokes' Theorem, you must first find the curl of the vector field. $\text{curl}(\mathbf{F}) = \square$ Now, use the curl to compute the circulation. $\text{Circulation} = \oint_C \mathbf{F} \cdot d\mathbf{r} = \square$