Point charge in non-periodic motion

Problem:

A charged particle A, moving with v << c, decelerates uniformly.  A second particle B has one-half the mass, twice the charge, three times the velocity, and four times the acceleration of particle A.  Find the ratio PB/PA of the powers radiated.

Solution:

Problem:

Electrons in a computer monitor CRT are accelerated to a final kinetic energy of 30 keV over a distance of 1 cm, then are rapidly decelerated to zero speed in collisions with the screen phosphor.  Assume both acceleration and deceleration are constant.  Consider the energy radiated by accelerated electrons (which has nothing directly to do with the light emitted by the phosphor).
(a)  Can this problem be treated non-relativistically?  Explain why or why not.
(b)  Develop an expression for the ratio r of the energy radiated during the acceleration phase, Erad, to the final kinetic energy Ekin, assuming constant acceleration a.  Also calculate a numeric value for r under the conditions pertaining to the acceleration of electrons in the monitor CRT described above.
(c)  Again assuming constant acceleration, estimate the maximum total fraction of kinetic energy that is radiated during the stopping of the electrons in the phosphor, and from that, the average power radiated per stopped electron in watts.  Assume all the kinetic energy is consumed in single collisions in a distance of 0.05 nm within single atoms of the phosphor.

Solution:

Problem:

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?

Solution:

Problem:

In a large region of space the electric field is constant and homogeneous, E = Ei, and gravity can be neglected.  A point mass m with charge q moves through the origin at
ti = 0 with velocity v = (v0cosα, 0, v0sinα), with v0 << c and cosα > 0.
At some later time tf  the x coordinate of the particle is L and the particle is still moving with vf  << c.
(a)  Find the z-coordinate of the particle at t = tf.
(b   Find the total energy radiate between ti and tf as a function of the variables given.

Solution:

Problem:

A ball with a total charge of 1 Coulomb and a mass 1 kg is dropped from the top of a tall building of height 100 m. What is the total power radiated as a function of height? (Ignore air friction).

Solution:

Problem:

A linear accelerator of length 10 m uniformly accelerates protons to kineticenergy 100 MeV.  Ignore relativistic effects.
(a) What is the power radiated by each proton (Watts)?
(b) What fraction of the energy imparted to the protons is lost to radiation?
(c) Sketch the normalized (1 = max) power pattern of the radiation [use a polar plot, indicate the direction of motion of the protons].

Solution: