GATE CE 2024 Set 2 — Question 11
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Engineering Mathematics → Partial Differential Equations → 2D Laplace Equation
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Question
A partial differential equationis defined for the two-dimensional field , inside a planar square domain of size 2 m × 2 m. Three boundary edges of the square domain are maintained at value , whereas the fourth boundary edge is maintained at .The value of at the center of the domain is
Correct answer
(B) 62.5
Solution
The given equation is Laplace's equation. For a square domain with constant values on each edge, the value at the center of the domain is the arithmetic mean of the values on the four boundary edges due to the mean value property of harmonic functions.Given and :
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