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# Q-Ans/Prob-Sol

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## CM-Mod11 :: Hamilton Jacobi Theory

Obtain solution of the free particle problem in two dimensions using Hamilton Jacobi equation and obtain expression for the Hamilton's principal function.

## Problem/EM-07013 Torque on current loopin magnetic field

A circular coil is formed from a  wire of length $L$ with $n$ turns. The coil carries a current $I$ and is placed in an external uniform magnetic field  $B$. Show that  maximum torque developed is  $\displaystyle\frac{IBL^2}{4n\pi}$.

## Problem/EM-2034 Application of Gauss law to an Integral

$$\newcommand{\Prime}{{{\,}^\prime}}$$
Approaching the problem of electric field for a uniformly charged sphere in two different ways, find the value of the integral $$\vec{\mathcal E} = \frac{1}{4\pi\epsilon_0} \iiint d^3r\Prime \frac{(\vec{r}-\vec {r}\Prime) } {|\vec{r}-\vec{r}\Prime|^3}.$$ where the integral runs over the volume of a sphere of radius $$R$$.