- #1

richyw

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## Homework Statement

Consider the Laplace’s equation, ∆u(r,θ) = 0, inside the quarter-circle of radius 2 (0 ≤ θ < π, 0 ≤ r ≤ 2), where the boundary θ is insulated, and [itex]u(r,\theta/2)=0[/itex]

Show that the insulated boundary condition can mathematically be expressed as

[tex]\frac{\partial u}{\partial \theta}u(r,0)=0[/tex]

## Homework Equations

## The Attempt at a Solution

It's insulated, so I think that means[tex]]\frac{\partial u(r,0)}{\partial t}=0[/tex]If we use separation of variables [itex]u(r,\theta)=\Phi(\theta)G(r)[/itex] then wouldn't insulated mean I need to take the time derivative of this, using the chain rule?