Homework Help a)Find the divergence of each and evaluate at the given point.[2.xz]A= -².z-x.yb) B=c)7.cos(sinZ2RC= 3.cos(p)cos(8) sin().cartesiancylindricalsphericalX:=1r:=3y:=24:=45°R: 0.5 8: 30 °Z:=3Z:=3$: 60°

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Find the divergence of each and evaluate at the given point. [2.x.z] a) A=-.z -x.y b) B= [7.cos(p) sin() 2 24 R c) C= 3.cos(p) cos(8).sin() cartesian X:=1 y:=2 cylindrical r:=3 spherical R: 0.5 Z:=3 4:=45° Z:=3 8: 30 ° : 60°

Find the divergence of each and evaluate at the given point. [2.x.z] a) A=-.z -x.y b) B= [7.cos(p) sin() 2 24 R c) C= 3.cos(p) cos(8).sin() cartesian X:=1 y:=2 cylindrical r:=3 spherical R: 0.5 Z:=3 4:=45° Z:=3 8: 30 ° : 60°

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter8: Symmetrical Components

Section: Chapter Questions

Problem 8.2P

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Concept explainers

Gradient of a Scalar Field

Consider a room or a place where the temperature is denoted by a scalar field T, such that at each point (x, y, z), the temperature is given as T(x, y, z). It is independent of time, in which the temperature rises most quickly. The gradient of T will show the direction at that point by moving away from (x, y, z). How far will the rise in temperature in that direction be determined by the gradient magnitude? Consider a surface that has a height above sea level at point (x, y) which is given by H(x, y). At that point, pointing in the direction of the steepest slope or grade is the gradient of H. The magnitude of the gradient of the vector gives the steepness of the slope at that point. How a scalar field changes in another direction can be measured by the gradient by taking a dot product rather than just the direction of the greatest change?

Question

Homework Help

a)
Find the divergence of each and evaluate at the given point.
[2.xz]
A= -².z
-x.y
b) B=
c)
7.cos(
sin
Z
2
R
C= 3.cos(p)
cos(8) sin().
cartesian
cylindrical
spherical
X:=1
r:=3
y:=2
4:=45°
R: 0.5 8: 30 °
Z:=3
Z:=3
$: 60°

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Step 1: Given

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Step 2: Find

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Step 3: Finding divergence of vector A

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Step 4: Finding divergence of vector B

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Step 5: Finding divergence of vector C

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