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Figure 2.1: |
Vector A= â A has a magnitude A=|A| and unit
vector â=A/A.
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Figure 2.2: |
Cartesian coordinate system: (a) base vectors x̂,
ŷ, and ẑ, and (b) components of vector A.
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Figure 2.3: | Vector addition by (a) the parallelogram rule and (b) the
head-to-tail rule.
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Figure 2.4: |
Position vector R12=P1P2= R2 -
R1.
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Figure 2.5: |
The angle θAB is the angle between A and B,
measured from A to B between vector tails. The dot product is positive
if 0 <= θAB < 90o, as in (a), and it is negative if
90o < θAB <= 180o, as in (b).
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Figure 2.6: |
Cross product AXB points in the direction n̂,
which is perpendicular to the plane containing A and B and defined by
the right-hand rule.
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Figure 2.7: | Geometry for Example 2-1.
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Figure 2.8: | Differential length, area, and volume in Cartesian
coordinates.
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Figure 2.9: |
Point P (r1, φ1, z1) in cylindrical coordinates; r1
is the radial distance from the origin in the x-y plane, φ1 is the
angle in the x-y plane measured from the x-axis toward the y-axis, and
z1 is the vertical distance from the x-y plane.
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Figure 2.10: | Differential areas and volume in cylindrical
coordinates.
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Figure 2.11: | Geometry of Example 2-3.
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Figure 2.12: | Cylindrical surface of Example 2-4.
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Figure
2.13: |
Point P(R1, θ1,
φ1) in spherical coordinates.
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Figure 2.14: | Differential volume in spherical coordinates.
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Figure 2.15: | Spherical strip of Example 2-5.
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Figure
2.16: |
Interrelationships between Cartesian coordinates (x, y,
z) and cylindrical coordinates (r, φ, z).
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Figure
2.17: |
Interrelationships between base vectors (x̂, ŷ) and
(r̂, φ̂).
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Figure
2.18: |
Interrelationships between (x,y,z) and (R,
θ, φ).
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Figure 2.19: |
Arrow representation for vector field E=r̂ r (Problem
2.18).
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