Chapter 6: Q12P (page 335)

Question: $\oint V \cdot dr$ around the circle ${(x - 2)}^{2} + {(y - 3)}^{2} = 9, z = 0$ where $V = (x^{2} + {yz}^{2}) i + (2 x - y^{3}) j$

Short Answer

Expert verified

The solution is derived to be $l = 18 π .$

Step by step solution

Given Information.

The given equation is $V = (x^{2} + y z^{2}) i + (2 x - y^{3}) j$ .

Definition of vector.

A quantity that has magnitude as well as direction is called a vector. It is typically denoted by an arrow in which the head determines the direction of the vector and the length determines it magnitude.

Apply Stokes’s theorem.

Apply Stokes' theorem, and the fact that $\nabla \times 2 yz \hat{j} + (- z^{2} + 2) \hat{k} = 2 \hat{k} as z = 0,$ and $n = \hat{k}$ then the solution is given below.

role="math" localid="1659262760807" $l = 2 \int_{σ} dσ = 2 (Area of circle) = 2 (9) π = 18 π$

Hence, the solution is derived to be $l = 18 π$ .

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Question: $\oint V \cdot dr$ around the circle ${(x - 2)}^{2} + {(y - 3)}^{2} = 9, z = 0$ where $V = (x^{2} + {yz}^{2}) i + (2 x - y^{3}) j$

Short Answer

Step by step solution

Given Information.

Definition of vector.

Apply Stokes’s theorem.

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Question: ∮V·draround the circle(x-2)2+(y-3)2=9,z=0whereV=(x2+yz2)i+(2x-y3)j

Short Answer

Step by step solution

Given Information.

Definition of vector.

Apply Stokes’s theorem.

One App. One Place for Learning.

Most popular questions from this chapter

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Question: $\oint V \cdot dr$ around the circle ${(x - 2)}^{2} + {(y - 3)}^{2} = 9, z = 0$ where $V = (x^{2} + {yz}^{2}) i + (2 x - y^{3}) j$