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You have a balloon filled with air that has the same temperature, pressure, density and composition as the environmental air at sea-level. You bring it on a drive from sea-level to the top of Mauna Loa (4,169 m). As you drive, the environmental air temperature drops according to the average tropospheric lapse rate and the volume of the balloon increases but it does not exchange heat with the environment (it's adiabatic).
When you reach the top of Mauna Loa, what is the temperature difference between the air inside the balloon and the environment?
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
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