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Geologists measure conductive heat flow out of the earth by drilling holes (a few hundred meters deep) and measuring the temperature as a function of depth. Suppose that in a certain location the temperature increases by 20°C per kilometre of depth and the thermal conductivity of the rock is 2.5 W/mK. What is the rate of heat conduction per square meter in this location? Assuming that this value is typical of other locations over all of the earth's surface, at approximately what rate is the earth losing heat via conduction?
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.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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