Q: The vector potential for a uniform magnetostatic field is / (r
The vector potential for a uniform magnetostatic field is / (r*B) (Prob. 5.25). Show that / in this case, and confirm that Eq. 10.20 yields the correct equation of motion.
See AnswerQ: Derive Eq. 10.23. [Hint: Start by
Derive Eq. 10.23. [Hint: Start by dotting v into Eq. 10.17.]
See AnswerQ: Evaluate the following integrals: (a) / where
Evaluate the following integrals: (a) / where a is a fixed vector, a is its magnitude, and the integral is over all space. (b) / where V is a cube of side 2, centered on the origin, and b= 4 yˆ + 3 zˆ...
See AnswerQ: Check that the retarded potentials of an oscillating dipole (Eqs.
Check that the retarded potentials of an oscillating dipole (Eqs. 11.12 and 11.17) satisfy the Lorenz gauge condition. Do not use approximation 3.
See AnswerQ: An insulating circular ring (radius b) lies in the xy
An insulating circular ring (radius b) lies in the xy plane, centered at the origin. It carries a linear charge density λ= λ0 sin φ, where λ0 is constant and φ is the usual azimuthal angle. The ring i...
See AnswerQ: A current I (t) flows around the circular ring in
A current I (t) flows around the circular ring in Fig. 11.8. Derive the general formula for the power radiated (analogous to Eq. 11.60), expressing your answer in terms of the magnetic dipole moment, m...
See AnswerQ: An electron is released from rest and falls under the influence of
An electron is released from rest and falls under the influence of gravity. In the first centimeter, what fraction of the potential energy lost is radiated away?
See AnswerQ: A positive charge q is fired head-on at a distant
A positive charge q is fired head-on at a distant positive charge Q (which is held stationary), with an initial velocity v0. It comes in, decelerates to v = 0, and returns out to infinity. What fraction...
See AnswerQ: In Bohr’s theory of hydrogen, the electron in its ground state
In Bohr’s theory of hydrogen, the electron in its ground state was supposed to travel in a circle of radius 5*10−11m, held in orbit by the Coulomb attraction of the proton. According to classical elec...
See AnswerQ: Find the angle θmax at which the maximum radiation is emitted,
Find the angle θmax at which the maximum radiation is emitted, in Ex. 11.3 (Fig. 11.13). Show that for ultrarelativistic speeds (v close to c), / /What is the intensity of the radiation in this maxima...
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