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LAPLACE’S EQUATION IN SPHERICAL COORDINATES

LAPLACE S EQUATION IN SPHERICAL COORDINATES With Applications to Electrodynamics We have seen that Laplace s EQUATION is one of the most significant equations in physics. It is the solution to problems in a wide variety of fields including thermodynamics and electrodynamics. In your careers as physics students and scientists, you will encounter this EQUATION in a variety of contexts. It is important to know how to solve Laplace s EQUATION in various coordinate systems. The coordinate systems you will encounter most frequently are Cartesian, cylindrical and SPHERICAL polar. We investigated Laplace s EQUATION in Cartesian COORDINATES in class and just began investigating its solution in SPHERICAL COORDINATES . Let s expand that discussion here.

This is the form of Laplace’s equation we have to solve if we want to find the electric potential in spherical coordinates. First, let’s apply the method of separable variables to this equation to obtain a general solution of Laplace’s equation, and then we will use our general solution to solve a few different problems.

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