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{{r|Spherical polar coordinates}}

{{r|Spherical polar coordinates}}

{{r|Spherical polar coordinates}}

{{r|Spherical polar coordinates}}

{{r|Spherical polar coordinates}}

{{r|Spherical polar coordinates}}

...rdinates by <math>x=r\cos\theta</math> and <math>y=r\sin\theta</math>. In polar coordinates, Laplace's equation is: ...coordinates are obtained from the components of <math>\nabla\phi</math> in polar coordinates:

...c is the radius of the great circle times this angle. Write in [[spherical polar coordinates]] the [[dot product]]

...f 1/''R'' are multiplied by angular functions depending on the [[spherical polar coordinates|spherical polar]] angles of '''R''' and also by coefficients with physical ...s in terms of [[spherical harmonics]], functions which depend on spherical polar coordinates. The Cartesian approach has the advantage that no prerequisite knowledge of

Take the origin of a [[spherical polar coordinates|spherical polar coordinate]] system in the center of symmetry of the charge ...r than the largest radius ''r''₁ of the shell); the [[Spherical polar coordinates#Infinitesimal surface and volume element|surface element]] is

{{Image|Spherical polar.png|right|250px|Spherical polar coordinates}} In [[mathematics]] and [[physics]], '''spherical polar coordinates''' (also known as '''spherical coordinates''') form a coordinate system for

The quantities {''r'', &theta;, &phi;} are known as [[spherical polar coordinates]] and its Jacobian is ''r''²sin&theta;. As an example we consider the spherical polar coordinates mentioned above. Here '''x''' = '''f'''('''t''') &equiv; '''f'''(''r'', &th

...dinates are written as ''x''^''j''. For example, for [[spherical polar coordinates]], ''x''¹ &equiv; ''r'', ''x''² &equiv; &theta;, ''x' ====Example: Sperical polar coordinates====

For instance, in the case of [[spherical polar coordinates]] ''r'', &theta;, and &phi;

...theta; are part of the solution of the [[Laplace equation]] in [[spherical polar coordinates]]. ...ta;-dependent part of the [[Laplace operator]] &nabla;&sup2; in spherical polar coordinates.

...practical advantage that the ''z&prime;''-axis has the usual [[spherical polar coordinates]] &alpha; &equiv; &phi; (longitude angle) and &beta; &equiv; &theta; (colat ...l modification of the previous proof. We start by retrieving the spherical polar coordinates <math>\omega_2\;</math> and

Here '''r''' has the spherical polar coordinates (''r'', &theta;, &phi;) and '''r''''

...rotor is usually described by means of [[spherical coordinates|spherical polar coordinates]], which form a coordinate system of 3-dimensional space. In the physics co ...is the [[Laplacian]]. The Laplacian is given above in terms of spherical polar coordinates. The energy operator written in terms of these coordinates is:

...cs''' are defined as solutions of the [[Laplace equation]] in [[spherical polar coordinates]]. There are two kinds of solid harmonic functions: the ''regular solid har Expression in spherical polar coordinates gives:

...all that in [[Spherical polar coordinates#Differential operators|spherical polar coordinates]]