A problem proposal for IPhO 2019 participants

All the best to all the 5 participants will be selected to represent India at IPhO 2019, to be held at Tel Aviv, Israel.

Here is a doable problem for you guys :P

A Dielectric slab of thickness $t$, relative permittivity $\epsilon_r$ is between two fixed metallic parallel plates. Faces of the slab and the plates are parallel. Distance between the plates is $d$. Find the minimum voltage applied between the plates sufficient to rupture the slab, if the breaking stress of slab is $\omega$. Consider a uniform string of length $l$, tension $T$, mass per unit length $\rho$ that is stretched between two immovable walls. Show that the total energy of the string, which is the sum of its kinetic and potential energies $E=\frac {1}{2}\int_0^1 [\rho (\frac {\partial y}{\partial t})+T (\frac {\partial y}{\partial x})^2]dx$. Where $y (x,t)$ is the string's transverse displacement relatively small. The general motion of the string can be represented as a linear superposition of the normal modes: that is $y (x,t)=\sum_{n=1,\infty}(Sin(n\pi\frac {x}{l}))Cos (n\pi\frac {vt}{l}-\phi_n)$. Here $v={\sqrt {\frac{T}{\rho}}}$. Demonstrate that $E=\sum_{n=1,\infty}E_n$, where $E_n=\frac {1}{4}m\omega_n^2A_n^2$ is the energy of $n^{th}$ normal mode. Here, $m=\rho l$ is the mass of the string, and $\omega_n=n\pi\frac {v}{l}$ is the angular frequency of the $n^{th}$ normal place. Note by Pawan Goyal
6 months ago

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@Archit Boobna @Rajdeep Dhingra best of luck for the TSTs of IPhO 2019.

- 6 months ago

Ya, best of luck. @Pawan Goyal, do you know them? How?

- 6 months ago