= Ohmic heating of a giant planet
{c}
{title2=$q=J^2/\sigma$}
Atmospheric winds across a magnetic field can induce electric currents. Their <Ohmic heating> converts mechanical energy into heat, at local rate $q=\mathbf J\cdot\mathbf E=J^2/\sigma$ in the simplest resistive description. To maintain <hot-Jupiter radius inflation>, current paths and deposited heat must influence the deep interior; dissipation restricted to optically thin upper layers need not maintain the planet's entropy.
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