Electromagnetic Theory I Problem Set 3 Due: 12 September 2011 9. The formula for the total energy stored in a static electric Feld U = ( ǫ0 / 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
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 09/25/2011 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.