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How to plot the graph between Q and J for the following equation? Here we can take $l$ = 1.

$\frac{\pi Q^2 + \sqrt{\pi^2 Q^4 + \frac{16 J^2}{l^2} }}{8} + \frac{2 J^2}{l^2 \bigg(\sqrt{\pi^2 Q^4 + \frac{16 J^2}{l^2}}\bigg)} - \frac{\pi}{4} Q^2 ln\bigg[ \frac{l}{8} \bigg(\pi Q^2 + \sqrt{\pi^2 Q^4 + \frac{16 J^2}{l^2} } \bigg) \bigg]=0$

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    $\begingroup$ Please post the Mathematica code. $\endgroup$
    – cvgmt
    Aug 9 at 7:59
  • $\begingroup$ The community expects from you: ❌: A clear description of an on-topic problem or goal. ❌: A minimal working Wolfram Language code example, formatted, easy to copy&paste, in Raw InputForm, $\LaTeX$ is excellent, but not enough. ❌. An example of what you expect as output. ❌. Some proof of minimal Mathematica knowledge. ❌. Minimum due diligence: Share how you have searched the site and documentation, your attempts and reasons to believe an answer exists. $\endgroup$
    – rhermans
    Aug 9 at 8:04

1 Answer 1

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ContourPlot[((Pi Q^2 + Sqrt[Pi^2 Q^4 + (16 J^2)/l^2])/8 + (2 J^2)/(
     l^2 (Sqrt[Pi^2 Q^4 + (16 J^2)/l^2])) - 
     Pi/4 Q^2 Log[l/8 (Pi Q^2 + Sqrt[Pi^2 Q^4 + (16 J^2)/l^2])] /. 
    l -> 1) == 2, {Q, -10, 10}, {J, -10, 10}, MaxRecursion -> 5]

plot

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