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8/18/2019 Conceptos de Clase de campos y ondas electromagneticas
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CONCEPTOS DE CLASE
Scalar: is a real number that serves for describe a magnitude.
2. Physical magnitude that expressed quantities with numbers.
Examples:o Temperature.
o Mass
o Electric charge
o Volume
o Time
o uic!ly
o Electric potential
o "istance between two points in a three dimensional space
o Magnitude of the gravitational force
o #nchanged mass
o
Energy$Momentum tensorMagnitude: quantity of length of a segment of straight or vector.
2. %nything that it can measure and it represents with a number.
Vector: is a segment of straight that it has magnitude& direction and sense.
Examples:o 'orce.
o (ravitational force.
o )peed.
o "isplacement.
Direction: measure of the angle that ma!es a line with the hori*ontal.
Rectangular coordinate system: is a system in which used rectangular
prisms for +nd a point in three dimensions.
−∞< x<∞ , −∞< y<∞ , −∞< z<∞
Cylindrical coordinate system: is a system that it used for de+ne the
position of a point in the space through an angle& a distance respect to an axis
and a height in the direction of the axis. -t used a cylinder for locate a point in
the space.
−∞< z<∞ & z is the cylinder center and the origin of the system.
−∞< ρ<∞ & ρ is the radio of the cylinder.
−∞<φ<∞ & φ is the a*imuthal angle.
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Spherical coordinate system: is a system that it used a sphere for locate a
point in the space.
0<θ<π & θ is the elevation angle and it is a solid angle a cone/& it is
measured from the *enith to the nadir.
0<φ<2π & φ is the a*imuthal angle.
Azimuthal angle: angle in degrees& it measured eastward from the north on
the hori*on.
• Part of a direction of reference and arrives to a line between the
observer and a point of interest provided in the same plane that the
direction of reference.
• -t is measured from the *enith to the nadir.
Nadir: is the lower point with relationship to observer and the celeste sphere.
enith: is the higher point whit relationship to observer.
!oint !roduct: it is de+ned as the multiplication of two vectors whose value is
equal to the product of the modules by the cosine of the angle between each
other.
-ts mathematical expression is0 A ∙ B= ABcosθ
-s called point product because in its notation is used a point to distinguish the
vector product.
Scalar !roduct: the scalar product of two vectors is a real number that
results from multiplying the product of its modules by the cosine of the angle. -tis well !nown that the result of the multiplication of vectors is a scalar.
!roduct "nner: the inner product of two vectors is a real number that is
obtained by multiplying the product of their modules by the cosine of the
angle.
a ∙ b=¿ a∨¿b∨cosθ
a ∙ b=(a1 , b1)∙(a2, b2)
¿(a1 , a2+b1, b2)
)i a=(2,1,3)
b=(1,2,2)
a ∙ b=(2,1,3)∙(1,2,2)
¿(2+2+6)
)i A=i+2 j+3 k
A=3 i+4 j+k
A ∙ B=( i+2 j+3 k )∙(3 i+4 j+k )
¿(i ∙3 i)+(2 j ∙4 j)+(3 k ∙ k )
¿3 i2+8 j
2+3 k 2
¿3(1)+8(1)+3(1)=14
i ∙ i=i2=1
j ∙ j= j2=1
k ∙ k =k 2=1
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2. -ce cube is placed at room temperature0
5. % bowl of water0
• -f the vector is large or small indicates how fast or slow growing function.
• 6owercase to uppercase for scalar and vector functions are used.
Di&ergence: measuring the di7erence between the in8ow and the out8ow in a
volume that encloses a volume element dV. -f the volume chosen contains only
source or sin! of a +eld& then the di7erence is non$*ero. The di7erence is the
di7erence of the lines who enter the volume with the amount of line exiting the
volume without returns to the surface.
The divergence is a scalar number is the result of two vectors in the timely
manner.
• artesian coordenates
Temperature0 the gradient vector indicates
the direction in which the temperature
The outer layers are what starts to melt and the
center is staying with lower temperature.
%t the bottom the pressure increases and
the surface decreases.
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∇ ∙ A=
∂ Ax
∂ x +
∂ Ay
∂ y +
∂ Az
∂ z
• ylindrical coordinates
∇ ∙ A= 1
ρ∂
∂ ρ ( ρAρ)+ 1
ρ∂ Aφ∂ φ + ∂ Az
∂ z
• )pherical coordinates
∇ ∙ A= 1
r2
∂(r2
Ar)∂ r
+ 1
rsenθ
∂(senθAθ)∂ θ
+ 1
rsenθ
∂( Ae)∂ e
The divergence is equal to the di7erence of incoming and outgoing forces.
The divergence measures the di7erence between an incoming and an outgoing
of a vector +eld on the surface surrounding 8ow& if the +eld has 9sources9 the
divergence is positive and if you have 9sin!s9 the divergence is negative
The divergence is 7 incoming vectors least 2 protrusions,the difference is -5.
* 7 incoming vectors
* 2 outbound (source)
Divergence 2-7 -5
!t is negative because it has more incoming than
outgoing flo"s.
The divergence is e#ual to $ because there are
% outgoing vectors and 5 starters.
: Divergence $ & 5 '$
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Curl: is the vector operator that shows the trend from a +eld to induce rotation
around a circulation point the vector on a closed path the edge of an area with
normal direction to itself when the area tends to *ero.
2. -s an axial vector whose magnitude is the maximum circulation of % by unit
area& as the area tends to *ero and whose direction is the normal direction of
area& when the area is oriented so that it result the maximum circulation.
The inflo" number is the same number of
outflo".
: Div