Solve Laplace equation with boundary conditions

In summary, the task is to calculate the potential function and electric field for the region between two concentric cylinders. The inner cylinder has a potential of 0 at r = 0.015 m and the outer cylinder has a potential of 100 at r = 0.025 m. The equation used is \Delta (square ) V = 0 and the solution involves two unknowns and two boundary conditions. The final result for V is yet to be solved.
  • #1
tan90
22
0

Homework Statement


Calculate potential function and the electric field for the region between two concentric cylinders, where V ( inner cylinder) = 0 at r = 0.015 m and V(outer cylinder) = 100 for r = 0.025


Homework Equations


[tex]\Delta[/tex] (square ) V = 0



The Attempt at a Solution


so, V depends only on s, and we will just end up having two unknowns and we will need two boundary conditions that we already have.
am i right?
 
Physics news on Phys.org
  • #2
Yes, you have two unknowns and two boundary conditions...what do you get for V?
 
  • #3
i haven't actually solved it yet, but i am pretty sure that i can figure it out. thanks.
 

1. What is the Laplace equation and what does it represent?

The Laplace equation is a partial differential equation that describes how a scalar quantity (such as temperature, pressure, or electric potential) changes in a space. It represents the equilibrium state of a system, where the change in the quantity is equal to zero.

2. How is the Laplace equation used to solve boundary value problems?

The Laplace equation is used to solve boundary value problems by finding a solution that satisfies the equation and the given boundary conditions. The boundary conditions provide the necessary information to determine a unique solution to the equation.

3. What are the most common methods for solving the Laplace equation with boundary conditions?

The most common methods for solving the Laplace equation with boundary conditions are the method of separation of variables, the method of eigenfunction expansion, and the method of integral transforms.

4. How is the Laplace equation applied in different fields of science and engineering?

The Laplace equation has a wide range of applications in various fields of science and engineering, such as heat transfer, fluid mechanics, electromagnetism, and structural analysis. It is used to model and solve problems related to these areas, including the behavior of electric circuits, the flow of fluids, and the distribution of temperature or stress in a system.

5. What are some common boundary conditions used in solving the Laplace equation?

Some common boundary conditions used in solving the Laplace equation are Dirichlet boundary conditions, where the value of the solution is specified at the boundary, and Neumann boundary conditions, where the derivative of the solution is specified at the boundary. Other types of boundary conditions include mixed boundary conditions, periodic boundary conditions, and Robin boundary conditions.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
515
  • Advanced Physics Homework Help
Replies
11
Views
2K
  • Advanced Physics Homework Help
Replies
7
Views
786
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
13
Views
2K
  • Differential Equations
Replies
22
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
1K
Replies
1
Views
796
Replies
10
Views
3K
Back
Top