A droppler question: Calculating the frequency of sound waves.

An untethered(free) weather balloon travelling with the wind (at wind speed) emits a 1 khz sound wave. The wind is blowing with respect to the land due east at .25 times the speed of sound in air. If the free balloon is moving away (due east)from a tower at same height, what is the frequency of the sound detected at the tower? Take the speed of sound to be 340 m/s. Hints- draw a picture. what is the preferred reference frame?

Calculating electic potential charges on point particles.

Two point particles, each with charge Q, are placed at positions +- a x. A) What is the elctric potential anywhere along the y axis? B) How much energy does it take to move a thrid particle, charge Q, from infinity to a position in order to make an equilateral triangle among the charges? (ie. all edges have length 2a)

charge density...electric field...electric potential

A (infinitley long) cylindrical non-conducting tube, inner radius a and outer radius b, with charge density p0 sits in a vacuum. Find (show work and derive) and sketch a plot as a function of radius r: A) the charge density B) the total charge enclosed in a cylindrical gaussian surface of radius r C) the electric field D) the electric potential referenced to the axis (r=0)

capacitar....

consider a parallel plate capacitor with surface area A and spacing d between plates: A) express the electric field in terms of the capacitance C, the charge Q, and A and d. recall the capacitance is C=E0*A/d. B) derive the energy stored in the capacitor Uc, when it has a charge Q on it. Do this by connecting a resistor across it and calculating the amount of engery dissipated in the resistor over all time, assuming it started with charge Q. C) Express Uc in terms of the electric field in the capacitor and volume of the capacitor. Then show that Uc=uv where u=elipson(e)o*E^2/2 is the energy density associated with an electric field and v is the volume between the plates.

current density, magnetic field

A long conducting circular cylindrical tube(circular cylinder inner radius a outer radius b) carries a total axial current Io distributed through the conductor. Find and sketch a plot as a function of radius (show work) A) the current density J(r) B) The magentic field B(r)