$ \Rightarrow \frac{{ - 12a}}{{{x^{11}}}} = \frac{{ - 6a}}{{{x^5}}} \Rightarrow x = {\left( {\frac{{2a}}{b}} \right)^{\frac{1}{6}}}$
$\begin{gathered}
{U_{at}}\,equilibrium = \frac{a}{{{{\left( {\frac{{2a}}{b}} \right)}^2}}} - \frac{b}{{\left( {\frac{{2a}}{b}} \right)}} \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{b^2}}}{{a4}}\,and\,{U_{\left( {x = \infty } \right)}} = 0 \hfill \\
\end{gathered} $
$\therefore $ $D = 0$$ - \left( { - \frac{{{b^2}}}{{4a}}} \right) = \frac{{{b^2}}}{{4a}}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| List $I$ | List $II$ |
| $(A)$ Microwave | $(I)$ $400\,nm$ to $1\,nm$ |
| $(B)$ Ultraviolet | $(II)$ $1\,nm$ to $10^{-3}\,nm$ |
| $(C)$ $X-$Ray | $(III)$ $1\,mn$ to $700\,nm$ |
| $(D)$ Infra-red | $(IV)$ $0.1\,m$ to $1\,mm$ |
Choose the correct answer from the options given below:
(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ $SI$ units)