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A neutrino must pass within about 10^-18m of a quark to have any chance of interacting with it. Thus, the maximum target area that a quark presents to a neutrino is about 10^-36m^2. However, a neutrino moves so quickly and the weak interaction is so weak that experimentally only about 1 in 10^12 typical neutrinos passing a quark within this radius actually interacts significantly with it. Use this information and the fact that Avagadro's number of protons and/or neutrons has a mass of about 1g and the fact that the density of lead is about 11g/cm^3 to estimate the average distance (in light years) that a neutrino would travel through the lead before it interacts.
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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