- #1
MathematicalPhysics
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I need some help starting off on this question.
Electrostatic potential [tex]V (x,y)[/tex] in the channel [tex]- \infty < x < \infty, 0 \leq y \leq a[/tex] satisfies the Laplace Equation
[tex]\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2}= 0[/tex]
the wall [tex]y = 0[/tex] is earthed so that
[tex]V (x,0) = 0[/tex]
while the potential on the wall [tex]y = a[/tex]
[tex]V (x,a) = V_0 \cos{kx}[/tex] where [tex]V_0 , k[/tex] are positive constants.
By seeking a soln of an appropriate form, find [tex]V (x,y)[/tex] in the channel.
Electrostatic potential [tex]V (x,y)[/tex] in the channel [tex]- \infty < x < \infty, 0 \leq y \leq a[/tex] satisfies the Laplace Equation
[tex]\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2}= 0[/tex]
the wall [tex]y = 0[/tex] is earthed so that
[tex]V (x,0) = 0[/tex]
while the potential on the wall [tex]y = a[/tex]
[tex]V (x,a) = V_0 \cos{kx}[/tex] where [tex]V_0 , k[/tex] are positive constants.
By seeking a soln of an appropriate form, find [tex]V (x,y)[/tex] in the channel.