A charged plate in a water solution results in counterions, what is potential and distribution?

The situation is as follows: Put a charged plate in a solution - the sign of the charge doesn't matter - in response, counterions will form in the solution such that - at infinite - the total electric field cancels. However, nearer the plate, you have a distribution of these counterions that is determined by the potential - V - due to the plate and the counterions. You only have to worry about one dimension - the distance from the plate in the x direction. Solve for V and rho where rho (r) is charge density The formula for the potential is as follows (Sorry for writing it out like this, I don't have word and the posting thing turns Mathematica symbols to gibberish): d^2V/dx^2 = (1/... click for more

Proving Gauss Law for arbitrary charge.

Gauss law for arbitray charge distribution is proved in the four part problem. Look at the attached file for details.

measurment of physiology

The axial magnetic field at a distance from a magnet falls-off as l/d3(note: 3 is the power of d mean d cube its not multiplying with d) where d is the distance to the magnet. A small, strong, permanent magnet generates a magnetic field that is measured by a small probe placed on its axis. It is desired to use the strength of the measured field to find the position of the (slowly moving) probe. What is the minimum number of bits of an analogue to digital converter in order to measure position to a precision of l mm over a distance range from 10cm to 20cm. Give some practical considerations for improving the accuracy of measurement.

Some Questions About Basic Quantum Physics

1. According to the classical theory of physics, the energy radiated by a blackbody approached infinity as the wavelength of the emitted light approaches zero. a) Why is this considered a problem for classical physics? b) Max Planck solved this problem is 1990. What was the key to the solution? Please see attached for all questions.

Electrostatic field and potential.

I would appreciate help in completing the proof of the equation on the second line of the attached file.