Two point charges of equal magnitude are 8.1 cm apart. At the midpoint of the line connecting them, their combined electric field has a magnitude of 40 N/C .Find the magnitude of the charges.

1. The indices of refraction for the fast and slow axes of quartz with 589 nm light are 1.5462 and 1.5553, respectively.

   1. (a) By what fraction of a wavelength is the e-ray retarded, relative to the o-ray, for every

      wavelength of travel in quartz?

   2. (b) What is the minimum thickness of quartz needed to manufacture a quarter-wave plate

      (QWP)?

   3. (c) Imagine that the thickness found in part (b) turned out to be too thin for the QWP to be

      durable and you want to manufacture a QWP with a thickness of at least 0.725 mm. What will be the thickness of the thinnest possible QWP that will be larger than 0.725 mm?

Three capacitors having capacitances of 8.4 μF , 8.0 μF , and 4.8 μF are connected in series across a 34-V potential difference.

PART A- What is the charge on the 4.8 μF capacitor?

PART B- What is the total energy stored in all three capacitors?

PART C- The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination?

PART D- What is the total energy now stored in the capacitors?

WILL RATE ! THANK YOU IN ADVANCE

how would you use a loop of wire and a magnetic field to generate current in a loop? That is, discuss practical ways to change the magnetic flux through the loop. Relate this to how the electrical generators work that provides electrical power to your home

Part B: Which is higher, the initial state energy or the final state energy of the atom if n=1, n′=3?

Part C: For the hydrogen transition indicated below, with n being the initial state and n′ being the final state, is the transition an absorption or an emission?
n=6, n′=2.

Part D: Which is higher, the initial state energy or the final state energy of the atom if n=6, n′=2?

Part E: For the hydrogen transition indicated below, with n being the initial state and n′ being the final state, is the transition an absorption or an emission?
n=4, n′=5

Part F: Which is higher, the initial state energy or the final state energy of the atom if n=4, n′=5?

Part G: Finally, which of these transitions involves the largest energy photon?

- n=4, n′=5

- n=6, n′=2

- n=1, n′=3

1) Consider the following example of a quantum mechanical wavefunction for a particle of mass m moving in one dimension, where α and A are constants.
?(?, ?) = ?? − ?(?2 + ?ℏ?/?) ,

a) Normalize the wavefunction. Show your work.

b) At what value of x is there equal probability for the particle to be either to the left or to the right of that x? Show your work and explain.

c) For the wavefunction given, what must the potential V (x, t) be in order for Ψ(x, t) to satisfy the Schrodinger equation? What classical system has this kind of potential?

d) Calculate the expectation values of x, x2, p, and p2. Explain in words what each calculation means (how it is related to measurement).

e) Determine ?! and ?" and check if their product is consistent with the uncertainty principle.

Light of original intensity I0 passes through two ideal polarizing filters having their polarizing axes oriented as shown in the figure (Figure 1). You want to adjust the angle ϕ so that the intensity at point P is equal to I0/8.00.

A.)If the original light is unpolarized, what should ϕbe?

B.)If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the light reaches, what should ϕ be?

In the card game Poker, a royal flush is an unbeatable hand. It is composed of an ace, king, queen, jack, and 10 all of the same suit. There are four possible royal flushes:

A♣️, K♣️, Q♣️, J♣️, 10♣️.
A♠︎, K♠︎, Q♠︎, J♠︎, 10♠︎.
A♥️, K♥️, Q♥️, J♥️, 10♥️.
A♦︎, K♦︎, Q♦︎, J♦︎, 10♦︎.

As you may expect, the probability of being dealt a royal flush is incredibly tiny. "Any poker player who has ever been dealt a royal flush will remember it for the rest of his or her life."

There are other hands that are less impressive than a royal flush. The least valuable hand is a bunch of unrelated numbers (e.g. not the same, not in a row) of different suits. For example, the hand

4♦︎, 3♦︎, J♥️, 2♠︎, 7♦︎.

is worth almost nothing. Let's call it a "lousy hand."

It turns out that this is a good analogy to understand entropy. A specific hand that one is dealt is a microstate. The classification of the hand ("royal flush" versus "lousy hand") is a macrostate.

Explain the difference between "microstates" and "macrostates" in this poker analogy.

there is a sinusoidal message signal (f = 100 Hz).

Make amplitude modulation with carrier frequency of 10KHz. Use three different modulation depths / indices (0.2 /0.60/0.8).

Then demodulate this mixed signal (for these three cases) by try to get message signals. (need matlab codes and graphs)

A cyclotron is used to produce a beam of high-energy deuterons that then collide with a target to produce radioactive isotopes for a medical procedure. Deuterons are nuclei of deuterium, an isotope of hydrogen, consisting of one neutron and one proton, with total mass 3.34×10−27kg. The deuterons exit the cyclotron with a kinetic energy of 5.00 MeV .

1. What is the speed of the deuterons when they exit? Express your answer with the appropriate units.

2. If the magnetic field inside the cyclotron is 1.25 T, what is the diameter of the deuterons' largest orbit, just before they exit? Express your answer with the appropriate units.

3. If the beam current is 350 μA how many deuterons strike the target each second? Express your answer as the number of the deuetrons.

A project manager decided to use critical ratio (C/Rij for WP j of project i) to prioritize and schedule the remaining work packages to be done for three concurrent projects with the data in the table below. The technical sequence (precedence) are WP1>WP2>WP4>WP4, for each of the three projects. For an illustration, the first project is due by day 4. Its first work package requires 2 days at workstation 1.

Please do/answer the following:

a. Calculate the critical ratio for each work package

b. Sequence them by their critical ratio in their descending order

c. Identify the most critical work package

d. Identify the least critical work package

e. Schedule them on a Gantt chart

f. Identify the completion time expected for each project

g. Identify each project expected to be late, based on the schedule

h. Identify the make span for the entire set of three projects

A.) A highway is made of concrete slabs that are 17.1 m long at 20.0°C. Expansion coefficient of concrete is α = 12.0 × 10⁻⁶ K⁻¹.

f the temperature range at the location of the highway is from −20.0°C to +41.9°C, what size expansion gap should be left (at 20.0°C) to prevent buckling of the highway?

*Answer in mm

B.)

The George Washington Bridge crosses the Hudson River between New York and New Jersey. The span of the steel bridge is about 1.60 km. What might be the difference between the maximum span and minimum span over the course of a year, if the temperature can vary from a low of −15.0°F in winter to a high of 103°F in summer? Expansion coefficient of steel is α = 12.0 × 10⁻⁶ K⁻¹.

C.) In which equation did temperature have a greater impact

An elastic collision between two particles,one of mass M and the other of mass 4M.
Which particle feels a greater force?
Justify your answer mathematically