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Gravity vs. electricity *
(a) In the domain of elementary particles, a natural unit of mass is the mass of a nucleon, that is, a proton or a neutron, the basic massive building blocks of ordinary matter. Given the nucleon mass as 1.67 · 10-27 kg and the gravitational constant G as 6.67 · 10-11 m3/(kg s2), compare the gravitational attrac- tion of two protons with their electrostatic repulsion. This shows why we call gravitation a very weak force.
(b) The distance between the two protons in the helium nucleus could be at one instant as much as 10-15 m. How large is the force of electrical repulsion between two protons at that dis- tance? Express it in newtons, and in pounds. Even stronger is the nuclear force that acts between any pair of hadrons (includ- ing neutrons and protons) when they are that close together.
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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