Consider the situation of two particles which have equal but opposite charges, +Q and -Q. The particles have identical mass. Discuss the following situations in terms of their motion and the work done on them by the relevant field. Where relevant, also provide a short discussion of the implications of these effects on the properties of the charged particles. If necessary, include diagrams to illuminate your solution.

(a) For the positive charge, the charge is stationary, and it is placed in a uniform electric field directed to the right (the +x-direction).

(b) For the positive charge, the charge is moving upwards (the +y-direction), and it is placed in a uniform electric field directed to the right (the +x-direction).

(c) For the negative charge, the charge is initially stationary and it is placed in a uniform magnetic field directed to the right (the +x-direction).

(d) For the positive charge, the charge is moving upwards (in the +y-direction) at constant velocity, and it is placed in a uniform magnetic field directed to the right (the +x-direction).

List out at least two uses for an RC circuit and explain how the RC would affect the use.

Use a computer to make two plots of the Boltzmann, Fermi-Dirac, and Bose-Einstein distributions functions versus x=(LaTeX: \epsilon-\mu ϵ − μ )/kT. For one make both axes linear. For the other make the y-axis logarithmic, and indicate the x- and y- ranges where the distribution functions agree to better than one percent.

A long wire carrying a 6.0 A current perpendicular to the xy-plane intersects the x-axis at x=−2.3cm. A second, parallel wire carrying a 2.6 A current intersects the x-axis at x=+2.3cm.

1. The Cosmic Microwave Background and Prizewinning Cosmology

(a) How can we see the CMB if the photons were released 14 billion years ago? Shouldn't those photons be billions of light years away by now?

(b) Who was awarded the 2006 Nobel Prize for Physics? What was the prize for-- what were the results, and how were they obtained?

(c) Why are these results from part (b) important?

You are given a new puppy as a birthday present and are eager to play with her. However, you soon come to realize that your new puppy has other plans. She decides to ransack your room and go after anything she can grasp in her mouth. One of the items is a rigid ball that has 5 grams of liquid ethanol in it from an experiment you did in class. The hot breath of the puppy vaporizes 50% of the ethanol to create an air-ethanol mixture at 50°C. After a few minutes, she releases the ball and the air-ethanol mixture comes to a new equilibrium state at 30°C. Taking the total pressure inside of the ball to be 1 atm, estimate the percent of ethanol that condenses at the final state. [HINT: Think carefully about how much ethanol is in the vapor state before the actual process starts. This is your starting amount.]

Fans at a heavy metal band concert are subject to tunes at an intensity of 1.5 watt/m2. The density of dry air at 273K is 1.293 g/L and the speed of sound in dry air is 331 m/s.

a.) This sound intensity corresponds to what maximum pressure amplitude?

b.) The ear drum has a surface area of ~52 mm2. How much mass would be stacked on a surface area of this size to match the pressure associated with the 1.5 watt/m2 intensity music?

A physicist builds a parallel-plate capacitor with adjustable spacing between the plates. When the plates are at their initial separation, the capacitance is 7.00 µF.

(a) At this capacitance, the capacitor is connected to a 18.00 V battery. After fully charging, how much energy (in µJ) is stored in the capacitor?

(b) The battery is then disconnected. Without discharging the capacitor, the physicist then doubles the separation between the plates. At this point, how much energy (in µJ) is stored in the capacitor?

(c) Without changing this new separation between the plates, the capacitor is discharged, and then reconnected to the 18.00 V battery. Now, after fully charging, how much energy (in µJ) is stored in the capacitor?

A piece of equipment functions such that a hot reservoir at 605 K transfers 1150 J of heat irreversibly to a cold reservoir at a temperature of 296 K.

1)

What is the change in entropy of the hot reservoir?

ΔS_H = J/K

2)

What is the change in entropy of the cold reservoir?

ΔS_c = J/K

3)

What is the change in entropy of the whole universe due to this process?

ΔS = J/K

A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform charge density ρ0, and the “southern” hemisphere a uniform charge density −ρ0. Find the approximate field E(r,θ) for points far from the sphere (r ≫ R).

P.S. Please be as neat as possible.

DATA AND RESULTS

Mass of Ball: .059 kg

1. The potential energy of the object at its highest point _2.32_Trial #1

2. The kinetic energy of the object just before impact _2.32 _

3. The velocity of the object just before impact, using kinetic energy _8.87 _

4. The “kinetic energy” of the object just after impact _33.80_ (Hint: neglect air resistance and think about the height it rebounds to)

5. The “rebound” velocity of the object _10.62_

6. The loss in energy _0 + 2.32 = 33.80 + 0 + loss_

Trial #2

1. The potential energy of the object at its highest point _2.03_

2. The kinetic energy of the object just before impact _2.03_

3. The velocity of the object just before impact, using kinetic energy _8.30 _

4. The “kinetic energy” of the object just after impact _-32.97_

5. The “rebound” velocity of the object __

6. The loss in energy __

Trial #3

1. The potential energy of the object at its highest point _1.74_

2. The kinetic energy of the object just before impact _1.74_

3. The velocity of the object just before impact, using kinetic energy _7.68 _

4. The “kinetic energy” of the object just after impact _-1.28_

5. The “rebound” velocity of the object _6.59_

6. The loss in energy __

Can someone please help me on this to double check I am doing this correctly? Thank you!

The current theory of the structure of the Earth, called plate tectonics, tells us that the continents are in constant motion. Assume that the North American continent can be represented by a slab of rock 4200 km on a side and 25 km deep and that the rock has an average mass density of 2910 kg/m3 . The continent is moving at the rate of about 1.8 cm/year.

a-What is the mass of the continent? Answer in units of kg.

b- What is the kinetic energy of the continent? Answer in units of J.

c- A jogger (of mass 70 kg) has the same kinetic energy as that of the continent. What would his speed be? Answer in units of m/s.

A hiker travels 22.5 km at 45.0 degrees in 10.0 hrs on day one, 18.0 km at 75.0 degrees in 9.50 hours on the second day, and 13.0 km at 130.0 degrees in 7.50 hrs on the third day.

a) Find the resultant displacement, in magnitude and direction form, for the hiker.

b) Calculate the average speed the hiker has for the trip (don't take into account rest time).

c) Calculate the average velocity the hiker has for the trip (don't take into account rest time).

d) If the hiker traveled on a fourth day, what displacement must they make to have a resultant displacement displacement of 50.0 km at 90.0 degrees for all four day travel?

A scientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. So she creates a 7.5-m-long, 4.0-mm-diameter wire of the material, connects it to a 1.5 V battery, and measures a 5.0 mT magnetic field 1.0 mm from the surface of the wire.