b) Given this electric field, what will be the force on a sodium ion of charge +1.6x10-19 C inside the cell wall? (Also indicate the direction of this force, relative to the electric field.)

c) How much work does it take to move a sodium ion through the cell wall against this potential difference? Give your answer in Joules and eV.

d) What would the electric field in the cell wall be as a function of x if the potential was V(x)= 4.1x1023 x3 V?

2) It is known that certain fish can detect magnetic fields. Suppose the mechanism for this is the magnetic force acting on a collection of charge in the fish brain.
a) If the fish swims at 3 m/s and feels a force of 0.002 N in the earths magnetic field (3x10-5 T), how large is the charge deposit?

b) Draw a diagram indicating the direction the fish is swimming, the direction of the magnetic field (assume a uniform field) and the direction of the force on the fish.

3) It has been found that a magnetic field applied to a broken bone causes it to heal faster. Suppose a broken arm is to be inserted into a solenoid with 200 turns per meter.
a) What DC current is to be applied to get a constant 2T magnetic field (assuming the core is air)?
b) What Emf is induced in a wire loop embedded in the broken bone if an alternating current of 5cos(8t) A is applied to the solenoid? Assume the loop has an area of 0.008m2 and is perpendicular to the solenoid axis.

4) Inside a TV tube electrons travel in a beam of radius 0.03m at a speed of 2000m/s. 3000 electrons pass a point in the tube per second, each with a charge of e = 1.6x10-19 C.
a) What is the current due to the beam?

b) Find the current density (current per area) for the beam.

c) Use Ampere's law to find the magnetic field at points outside the beam as a function of distance from the beam center, r.

d) Use Ampere's law to find the magnetic field at points inside the beam as a function of distance from the beam center, r.

5) The displacement of molecules in a liquid as a sound wave passes through it is given by s(x,t) = C cos (kx - t) where C = 0.002m, k = 20 rad/m, and  = 8000rad/s.
b) What is the maximum displacement of a molecule in the liquid from equilibrium?

c) What is the frequency of vibration of a molecule in the liquid?

d) What is the speed of the wave?

e) What is the wavelength of the wave?

f) What is the velocity of a molecule in the liquid as a function of time?

6) A hydrogen discharge tube emits light in the visible spectrum at four discrete wavelengths: the H line at = 656.3 nm, the H line at = 486.1nm, the H line at = 434.1nm, and the H line at =410.2nm.
a) If a collimated beam of light from a hydrogen dischage tube is incident normally on a diffraction grating with slit spacing of 1.9 m, what are the angles that locate the first- and second-order maxima for these hydrogen lines? (2d sin ym = m (m = 1, 2, 3...)

b) What is the energy of each photon? (E=hf)

c) All the visible lines have a final n value of 2. What is the starting energy level quantum number, n, for each of these photons? (E=13.6 eV/n2)

7) Electrons are ejected from a metallic surface with speeds ranging up to 4.60x105 m/s when light with a wavelength of l = 625 nm is used.
a) What is the work function of the surface in eV?

b) What is the cutoff frequency for this surface?

c) Give some examples of everyday devices which use the photo-electric effect.

8) The resolving power of a microscope depends on the wavelength used. To 'see' an atom from a distance of 20 cm would require an angular limit of resolution of 5.00x10-9 radians.
a) If the microscope opening is 0.005m, what wavelength of light would be needed?

b) What speed of electron would be needed if the microscope was an electron microscope?

c) Why would you be willing to buy the electron microscope but not the optical one?

Bonus:
Explain why oil slicks sometimes have pretty colors?

In the falling magnet experiment (to prove Faraday's law) what happened to the graph on the calculator when the magnet was turned over and allowed to fall? Why?

For one point each, what information can we get once you determine the wavefunction, , the solution to Schrödinger's equation (not the 4 quantum numbers, you get those when you solve for )?