Tutorial 14: Laplaceβs Equations
- Solve the Laplace's equation for a rectangular plate
subject to the given boundary conditions
Solution
Using and as a separation constant leads to
and
Then
for so that
Imposing
gives
so that
where
- Solve the Laplace's equation for a rectangular plate
subject to the given boundary conditions
Solution
Using and as a separation constant leads to
and
Then
for and
for so that
Imposing
gives
and
for so that
- Solve the Laplace's equation for a rectangular plate
subject to the given boundary conditions
Solution
Using and as a separation constant leads to
and
Then
for so that
Imposing
gives
for so that
Note that the question changed for Question 4
- Solve the Laplace's equation for a rectangular plate
subject to the given boundary conditions Answer:
Solution
This boundary-value problem has the form of Problem 2 in this section, with and . Thus, the solution has the form
The boundary condition implies
and
The boundary condition implies
and