Chapter 6: Q13P (page 335)

$\iint (2 xi - 2 yj + 5 k) \times ndσ$ over the surface of a sphere of radius $2$ and center at the origin.

Short Answer

Expert verified

The solution derived is $I = 0$ .

Step by step solution

Given Information.

The given expression is $\iint (2 xi - 2 yj + 5 k) \times ndσ$ .

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 its magnitude.

Apply divergence theorem.

Apply the divergence theorem and the fact that $\nabla \times V = 2 - 2 = 0$ then the integral becomes as shown below.

$I = 0 \times ∭_{V} dτ$

$= 0$

Hence, the solution derived is $I = 0$ .

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$\iint (2 xi - 2 yj + 5 k) \times ndσ$ over the surface of a sphere of radius $2$ and center at the origin.

Short Answer

Step by step solution

Given Information.

Definition of vector.

Apply divergence theorem.

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∬(2xi−2yj+5k)×ndσover the surface of a sphere of radius 2and center at the origin.

Short Answer

Step by step solution

Given Information.

Definition of vector.

Apply divergence theorem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

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Study anywhere. Anytime. Across all devices.

$\iint (2 xi - 2 yj + 5 k) \times ndσ$ over the surface of a sphere of radius $2$ and center at the origin.