How Do You Determine the Gradient in Spherical Coordinates?

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The spherical coordinate system is the method of giving the specific direction of a point in a three dimensional space. The coordinates are represented by rho, theta and phi. The coordinates are first changed into rectangular coordinates. This is done in order to simplify the initial equation. The equation is then partially differentiated to determine the gradient.

The gradient is a concept used to generalize a function’s derivative in one dimension to a function in numerous dimensions. The spherical coordinate system is more convenient in the creation of points in three dimensional space. Rho is the measured distance from the origin to the point, theta is the angle from the origin on the x axis to the line connecting the point, and phi is the angle between the point and the point from the z axis. The partial derivatives are then multiplied by specific vectors in the coordinate systems. These vectors are the simple directions from the point of origin to the given specified point through any of the three axes in the dimension space. The unit vector in most cases is assumed to be u.

The multiplication by the unit vector is the final step towards obtaining the gradient in a spherical coordinate system.