a muonic atom has an electron replaced by a particle called a muon, which is about 200 times more massive, but otherwise almost the same as an electron before you start the rest of this, you'll want to check what quantities for a bohr hydrogen atom depend on the electron mass. consider a muonic hydrogen atom in its ground state. ignore subtle effects like the reduced mass or any relaticistic considerations (even though the former should be relevant here). Remember that in a bound electrostatic system the kinetic energy is equal to the opposite of the total energy. Calculate:

a) The orbital frequency and the wavelength corresponding to classical electron-magnetic waves of this frequency

b) The frequency and wavelength of a photon with just enough energy to ionize the system

c) The de broglie wavelength and the de broglie frequency for the muon

d) Another relevant length scale is the so-called "compton wavelength" of the muon, which is the wavelength corresponding to the rest-energy of the particle assuming the speed of light. calculate the compton wavelength of the muon e) yet one more relevant length scale is the radius of this atom, a0(u). Taking this length as an uncertainty on where the muon might be found, what is the minimum uncertainty on momentum?

Congratulations! You have just inherited 250 acres of land in south Texas. An oil company approached you and offered you a one 1/2 percent (0.005) royalty for the rights to your oil. Given the following information, answer the questions below. Size = 250 acres Porosity of oil zone rock = 20 % Recoverable Oil = 30 % You do not need to consider the cost of the wells. Thickness of oil zone = 20 feet Oil saturation in pores = 40 % Life of the wells = 30 years Helpful conversions 1 acre = 43,560 square feet 1 cubic foot = 0.178 barrels

1. How many barrels of oil are in the ground?

2. How many barrels of oil are recoverable?

3. What is the value of recoverable oil at $95 per barrel?

4. What is the value of recoverable oil at $30 per barrel?

5. How much total money do you expect if oil stays at $95 per barrel?

6. How much total money do you expect if oil stays at $30 per barrel?

7. What will be your average monthly royalty check at $95 per barrel?

8. What will be your average monthly royalty check at $30 per barrel?

1. In a system design the electrons are accelerated from rest through a potential difference of 250 V. The electrons travel along a curved path because of the magnetic force exerted on them, and the radius of the path is measured to be 5 cm long. If the magnetic field is perpendicular to the beam what is the linear speed of the electrons, what is the angular speed of the electrons and what is the magnitude of the magnetic field in this system, respectively?

A. 9.4 x 106 m/s, 188 x 106 rad/s, 107.5 x 10-6 T
B. 2.4 x 103 m/s, 2.61 x 105 rad/s, 13.6 x 10-4 T
C. 6.8 x 107 m/s, 1.82 x 107 rad/s, 22.7 x 10-3 T
D. 1.2 x 107 m/s, 214 x 107 rad/s, 9.4 x 10-4 T

2. What is the direction of magnetic force created by a moving particle?
A. Same direction with the velocity of the particle
B. Same direction with the magnetic field
C. Direction of the vectoral product of charge of the particle and the magnetic field
D. Direction of the vectoral product of velocity of the particle and the magnetic field

3.

What is the magnetic force created by a current carrying wire? (Please choose two corrert answers)

A. Different than zero on a closed loop  
B. Zero on a closed loop  
C. Depends on the angle between the length vector and magnetic field lines  
D. Depends on the angle between the length vector and velocity vector

4.

What did Oersted discovered?

A. Magnetic force created by a closed loop
B. Magnetic force of a charged particle
C. Compass needle is deflected by a current carrying wire
D. Magnetism of a charged particle

Interstellar gas in many galaxies is in virial equilibrium with the stars, in that the rms speed of the gas particles is the same as the rms stellar speed. Consider a large elliptical galaxy with a virial radius of 150 kpc and a mass of 5 × 10¹² solar masses. Calculate the rms stellar velocity using the virial theorem. Hence estimate the temperature of the interstellar gas, assuming that it is composed entirely of hydrogen.

Two children are sliding down a snowy hill which is inclined by 45.6 degrees with respect to horizontal. One has a rough sled which has a coefficient of kinetic friction between it and the snow of uk = 0.364; the other has a slippery sled which has a coefficient of kinetic friction between it and the snow of uk = 0.138. If both children start at the top of the 46.3 m tall hill initially at rest, what is the difference in speed between these two sleds at the bottom of the hill?

k=9.00*10^9 Nm^2/C^2. Pay attention to unit conversions.

In one experiment the electric field is measured for points at distances r from a very long, straight line of charge that has a charge per unit length λ. In a second experiment, the electric field is measured for points at distances from the center of a uniformly charged insulating sphere that has total charge Q and radiusR = 8.00 mm. The results of the two measurements are listed in the table below, but you are not told which set of data applies to which experiment.

To solve the mystery, start by creating the graph ln(E) versus ln(r) for each data set. Make sure you convert r values to meters before calculating ln(r).

Use Excel. The axes should be labeled appropriately, and the graphs should be titled Measurement A and Measurement B, respectively. Show a linear trendline and its equation for each graph. Make sure that the numerical coefficients of the trendline equation show at least five significant digits, you will need them in your calculations below. You will submit the Excel file showing the graphs to Blackboard, separate from the test. (5 points)

Now answer the following questions:

1. a) Use these graphs to determine which data set, A or B, is for the uniform line of charge and which set is for the uniformly charged sphere. Explain your reasoning.

2. b) Use the trendline equation of the graph corresponding to the line of charge to calculate λ. Show neatly your calculations.

3. Use the trendline equation of the graph corresponding to the charged sphere to calculate Q. Show neatly your calculations.

4. Calculate the electric field inside the sphere, at 4.00 mm from the center. Show neatly your calculations.

Hint: If the electric field is invers proportional to a power of r, say E = B/rn with B a constant factor, then ln(E) = ln(B) - n∙ln(r). So, the graph of ln(E) versus ln(r) should be a straight line, for which the slope is -n and the vertical intercept is ln(B).
Now apply this idea to the electric field of a line of charge for which E = 2kλ/r, so ln(E) = ln(2kλ) - ln(r), and to the electric field outside of a uniformly charged sphere for which E = kQ/r , so ln(E) = ln(kQ) -2ln(r). What is left for you is to compare these theoretical equations to the trendline equations of the charts and identify which one applies best to Measurement A and which one to Measurement B.

1. Consider the following situation. With the power supply off, the current limit one-half of a turn and the voltage knob completely counterclockwise, a coil is connected to it. A secondary coil is placed just in front and connected it to a galvanometer. If you gently increase the voltage of power supply, explain what you would observe in the galvanometer. Would the needle deflect? Why?

2. If the secondary coil is moved away from the primary coil, would the deflection of the needle be larger, smaller, or the same? Explain!

3. In this experiment, you moved the bar magnet closer to or away from the coil while keeping the coil stationary. How would the result change if the moved the coil while the bar magnet is kept at rest? Explain!

If you move both the bar magnet and the coil, how would this motion change the result you observed in this experiment. Explain!

Two thin square flat sheets are placed parallel to each other. The distance between the sheets is much smaller than the size of each sheet, so we can consider the sheets infinite. The sheets are uniformly charged, with surface charge densities σ1 and σ2, respectively. The magnitudes and the signs of these charge densities are not known. To determine σ1 and σ2, you measure the electric force on a test point charge q = 2.00 nC at several locations. You find the following results:

i) When the test charge is placed in the region between the sheets, the electric force is 7.92 mN (mili Newtons) and is directed towards sheet 2.

ii) When the test charge is placed in the regions outside, on either side of the sheets, the electric force is 1.12 mN and is directed towards the sheets.

Now address the following questions:

a) Calculate the electric field in the region between the sheets and then in the outside regions. Draw the sheets and sketch some electric field lines in all three regions.
Show neatly your calculations. (15 points)

b) Determine σ1 and σ2. Express your results for σ1 and σ2 in nC/cm2 and do not forget to include the sign. Show neatly your calculations. (20 points)
(Hint: start by expressing the electric fields you just calculated in part a in terms of σ1 and σ2, keeping in mind the principle of superposition. Then solve for the charge densities.)

[Formulas to use: Esheet = 2πk|σ|; F = qE, and the principle of superposition]

A proton moves with a speed of 0.895c.

(a) Calculate its rest energy. _____MeV

(b) Calculate its total energy. ____GeV

(c) Calculate its kinetic energy._____GeV

A radar station locates a sinking ship at range 19.5 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 166° clockwise from north, with elevation 1.95 km.

(a) Write the displacement vector from plane to ship, letting î represent east, ĵ north, and k up.

(b) How far apart are the plane and ship? 2 km