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The electric field E at distance r from the center of a uniformly charged sphere of radius R and total charge Q is E= Qr/4ΠεoR^3 when r<R. Such sphere corresponds to the Thomson model of the atom. Show that an electron placed in the center of the sphere will executes simple harmonic motion if it is displaced from the center.
a. Derive the frequency of this motion.
b. Assuming that the spectrum of Hydrogen is produced by the oscillating electron moving in simple harmonic motion, Compare the formula derive in part(a) with the actual hydrogen spectrum.
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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