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emhw03 - Electromagnetic Theory I Problem Set 3 Due 12...

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Electromagnetic Theory I Problem Set 3 Due: 12 September 2011 9. The formula for the total energy stored in a static electric Feld U = ( ǫ 0 / 2) i d 3 x E 2 includes the self-energy of the charges as well as their mutual potential energy. As discussed in class the self-energy of a point charge is inFnite. Study this issue for a single charge Q by spreading out a point charge in two di±erent ways: a) Replacing the point charge by a uniformly charged spherical surface of radius δ and b) Replacing the point charge by a uniformly charged ball of radius δ . In each case, Fnd the electric Feld everywhere and evaluate the integral deFning U . Classical physics puts no apriori limit on how small δ could be. However, relativistic quantum mechanics implies that a particle’s location cannot be known within a distance smaller than its Compton wavelength p /mc . ²or cases a) and b), assume δ = p /mc to get an estimate for the self energy of the electron. 10. The standard capacitor used in electrical circuits has only two conducting plates and is
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