Is there a simple mathematical way of proving the left hand side equals the right hand side (see attached image)?(adsbygoogle = window.adsbygoogle || []).push({});

Any help will be much appreciated as I'm desperately trying to work out exactly where the magnetic Reynolds number comes from. I can derive the left hand side (its simply the ratio of advection term to the diffusion term which themselves can be derived using Maxwell's equations) but I am stuck at this final step as I'm not very good at vector calculus.

Thanks in advance for any help.

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# Magnetic Reynolds Number

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