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A charged particle accelerated in a circular orbit loses energy according to the following equation (developed by Schwinger). energy lost per revolution \( =12 \pi e^{2}\left(\frac{E}{m_{o} c^{2}}\right)^{4} \times 10^{9} \mathrm{~J} \) Determine the energy loss for: (a) a \( 50 \mathrm{MeV} \) electron in an orbit with a radius of \( 2 \mathrm{~m} \) (b) a \( 50 \mathrm{MeV} \) proton in the same orbit.

Data: Energy of the charged particles (E) = 50 MeV = 8 * 10-12 J Mass of an electron