Chapter 6: Q21P (page 336)

Find vector fields A such that $V = curlA$ for each given V.
$V = - K$

Short Answer

Expert verified

The vector field is derived to be $A = iy + \nabla u$ .

Step by step solution

Given Information.

The given equation is $V = - k$ .

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 the vector and the length determines it magnitude.

Find the vector field.

In this problem find the vector A whose curl gives the vector.

$V = - K$

The components of the vector V are given in terms of the derivatives of A .

role="math" localid="1659242905787" $\frac{\partial A_{z}}{\partial y} - \frac{\partial A_{y}}{\partial z} = 0 \frac{\partial A_{x}}{\partial z} - \frac{\partial A_{z}}{\partial x} = 0 \frac{\partial A_{z}}{\partial y} - \frac{\partial A_{y}}{\partial z} = 0 \frac{\partial A_{y}}{\partial x} - \frac{\partial A_{x}}{\partial y} = - 1$

An obvious solution is mentioned below.

$A = iy + \nabla u$

Here is an arbitrary function.

Hence, the vector field is derived.

$A = iy + \nabla u$

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Find vector fields A such that $V = curlA$ for each given V.
$V = - K$

Short Answer

Step by step solution

Given Information.

Definition of vector.

Find the vector field.

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Find vector fields A such that V=curlAfor each given V.V=-K

Short Answer

Step by step solution

Given Information.

Definition of vector.

Find the vector field.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Modern Physics

Quantum Physics

Classical Mechanics

Circular Motion and Gravitation

Energy Physics

Oscillations

Study anywhere. Anytime. Across all devices.

Find vector fields A such that $V = curlA$ for each given V.
$V = - K$