Question

A cube of side $1m$ whose base is rigidly fixed to the surface in contact is given a charge $Q=2C$ at its top surface. [Charge is uniformly distributed on top surface only].
Electric field of $50N/C$ also exist as shown in figure. Elastic energy stored in cube if modulus of rigidity is $3\times {10}^{10}N/m^{2}isx\times {10}^{-8}J.$ Find $x$ upto two decimal points

Answer 1

$Energy=\frac{1}{2}\times stress\times strain\times volume$
$\eta =\frac{stress}{strain}$
$Energy=\frac{1}{2}\frac{(stress{)}^2}{\eta }\times \left(volume\right)$
$Stress=\frac{F}{A}=\frac{QE}{a^2}$
$Energy=\frac{1}{2}{\left(\frac{QE}{a^2}\right)}^2\times \frac{a^3}{\eta }=\frac{1}{2}\frac{Q^2{E}^2}{\eta a}$
$\cup =\frac{2^2\times {50}^2}{2\times 3\times {10}^{10}\times 1}=16.67\times {10}^{-8}J$