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ELECTROMAGNETIC FIELDS AND THEORY: FIELDS AND VECTORS: Spherical
Coordinates 1.2.3 Spherical. In figure [5], a point P will be identified throughout the coordinates, rp , θp , φp (19)
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The
unitary vectors that indicate the direction in which the coordinates grow
are:
none of the unitary
directions remains constant in all the point and must be,
the differential
displacements along the above directions will be,
dr r
dθ r senθ dφ (22)
a generic
displecement of point P,
In figure [6],
a differential volume element is shown as well as the differential elements
of area that encloses it. The differential element of volume is equal to, dV = r2 senθ dr dθ dφ (24)
the perpendicular faces to axis r, have a
differential area equal to,
dSr = r2 senθ dθ dφ
(25)
the area of the
faces perpendicular to direction θ,
dSθ = r senθ dφ dr (26)
and the area
of faces
perpendicular
to to φ direction,
dSφ = r dθ dr (27) Like all the
other systems of coordinates,
any
element of area described can be expressed through a vector with a magnitude
equal to the area and with a direction perpendicular to the element. |
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