The Seperation of Variables
Not what you're looking for?
Solve Laplace's equation by separation of variables in cylindrical coordinates. Assume symmetry about the z axis and no z dependence.
Check the result by comparing to an infinite line charge.
Purchase this Solution
Solution Summary
This solution solves Laplace's equation for the separation of variables.
Solution Preview
Please see the attachment for the solution.
Laplace's equation in polar coordinates is:
(1.1)
We assume that the potential can be written as a product of independent single-variable functions, namely:
(1.2)
Then, substituting this back in (1.1) the partial derivatives become full derivatives and we obtain:
Dividing both sides by we separate the equation:
(1.3)
Since the functions are completely independent, the only way equation (1.3) can be true for all values of r and is if both sides equal the same constant k.
So from the angular equation we get:
(1.4)
And the radial equation becomes:
(1.5)
Case 1:
The ...
Purchase this Solution
Free BrainMass Quizzes
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
Basic Physics
This quiz will test your knowledge about basic Physics.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.
The Moon
Test your knowledge of moon phases and movement.
Variables in Science Experiments
How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.