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The muons created by cosmic rays in the upper atmosphere rain down uniformly on the earth's surface, although some of them decay on the way down, with a half-life of about 1.5?s (measured in their rest frame). A muon detector is carried in a balloon to an altitude of 2000m, and in the course of one hour detects 650 muons traveling at 0.99c towards the earth. If an identical detector remains at sea level, how many muons will it register in one hour? (Remember that after n half-lives, 2^(-n) of the original particles survives).
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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