Magnetic buoyancy ($p_{\mathrm{in}}+B^2/(2{\mu }_0)=p_{\mathrm{out}}$)

Magnetic buoyancy is the tendency of magnetized fluid to rise when magnetic pressure support reduces its density relative to its surroundings. For a thin flux concentration in lateral balance, $p_{\mathrm{in}}+B^2/(2{\mu }_0)=p_{\mathrm{out}}$. At equal temperature and composition an ideal-gas equation of state then gives ${\rho }_{\mathrm{in}}<{\rho }_{\mathrm{out}}$, producing an upward buoyant force. Thermal exchange, magnetic tension and stable stratification modify this simple argument. In a solar dynamo, buoyant toroidal flux can emerge as tilted bipolar active regions.