Conceptos de Clase de campos y ondas electromagneticas

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.



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



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.



∇ ∙ 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 '$



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

Conceptos de Clase de campos y ondas electromagneticas

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