Chapter 6: Q6P (page 334)

$\iint V \times ndσ$ over the closed surface of the tin can bounded by if $x^{2} + y^{2} = 9, z = 0, z = 5$ if $V = 2 x y i - y^{2} j + (z + x y) k$ .

Short Answer

Expert verified

The solution derived is $I = 45 π$ .

Step by step solution

Given Information.

The given expression is $x^{2} + y^{2} = 9, z = 0, z = 5,$ if $V = 2 xyi - y^{2} j + (z + xy) k$ .

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 a vector and the length determines its magnitude.

Apply the divergence theorem.

$∮_{+ \partial V} V \times ndσ = \int_{V} \nabla \times Vdτ$

But $\nabla \times V = 2 y - 2 y + 1 = 1$ then the integral becomes as shown below.

$I = \int_{V} dτ = π (3^{2}) (5)$

$= 45 π$

Hence, the solution derived is $I = 45 π$ .

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$\iint V \times ndσ$ over the closed surface of the tin can bounded by if $x^{2} + y^{2} = 9, z = 0, z = 5$ if $V = 2 x y i - y^{2} j + (z + x y) k$ .

Short Answer

Step by step solution

Given Information.

Definition of vector.

Apply the divergence theorem.

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∬V×ndσover the closed surface of the tin can bounded by if x2+y2=9,z=0,z=5ifV=2xyi−y2j+(z+xy)k.

Short Answer

Step by step solution

Given Information.

Definition of vector.

Apply the divergence theorem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Magnetism

Atoms and Radioactivity

Mechanics and Materials

Geometrical and Physical Optics

Medical Physics

Study anywhere. Anytime. Across all devices.

$\iint V \times ndσ$ over the closed surface of the tin can bounded by if $x^{2} + y^{2} = 9, z = 0, z = 5$ if $V = 2 x y i - y^{2} j + (z + x y) k$ .