Section: Engineering Mathematics | Marks: 2
Linked Answer Q.27 & Q.28: The potential $u(x,y)$ satisfies the equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ in the square $0 \le x \le \pi$, $0 \le y \le \pi$. Three of the edges $x = 0$, $x = \pi$ and $y = 0$ of the square are kept at zero potential and the edge $y = \pi$ is kept at nonzero potential. If the edge $y = \pi$ is kept at the potential $\sin x$, then the potential $u(x,y)$ is given by
- A. $u(x,y) = \sum_{n=1}^\infty \frac{\sin nx \sinh ny}{\sinh n\pi}$
- B. $u(x,y) = \frac{\sin x \sinh y}{\sinh \pi}$
- C. $u(x,y) = \frac{\sin x \cosh y}{\cosh \pi}$
- D. $u(x,y) = \sum_{n=1}^\infty \frac{\cosh nx \sin ny}{\cosh n\pi}$