Give a brief introduction on Poisson’s and Laplace’s Equations.
Answers
Answered by
1
In the subjects of gravitation, mechanical engineering, physics, electrostatics the two equations are used.
Poisson's equation is a generalization of the Laplace equation.
Poisson's equation describes the gradient of potential field V (electrostatic or gravitational) in terms of volume mass (or charge) density ρ. The Delta operator means the 2nd degree partial derivative in x, y, and z directions.
In general the volume charge density in space is in real situations is not known exactly. Only the boundary values on a closed boundaries (surface) are known. So this PDE (partial differential equation) along with boundary values is used to derive an expression for potential V at all points inside a closed surface.
When the function on the RHS = f = 0 or volume charge density = 0, then the equation becomes Laplace's equation.
This equation is also used in Heat transfer problems to determine temperature in a medium at all points when heat transfers take place from one end to another.
For a linear medium (linear density distribution) these equations can be derived from Gauss's law. Using the potential the field intensity or strength is also determined.
Poisson's equation is a generalization of the Laplace equation.
Poisson's equation describes the gradient of potential field V (electrostatic or gravitational) in terms of volume mass (or charge) density ρ. The Delta operator means the 2nd degree partial derivative in x, y, and z directions.
In general the volume charge density in space is in real situations is not known exactly. Only the boundary values on a closed boundaries (surface) are known. So this PDE (partial differential equation) along with boundary values is used to derive an expression for potential V at all points inside a closed surface.
When the function on the RHS = f = 0 or volume charge density = 0, then the equation becomes Laplace's equation.
This equation is also used in Heat transfer problems to determine temperature in a medium at all points when heat transfers take place from one end to another.
For a linear medium (linear density distribution) these equations can be derived from Gauss's law. Using the potential the field intensity or strength is also determined.
Attachments:
Similar questions