An infinitely long, solid non-conducting rod (cylinder) with circular cross section of radius a has its axis along the z-axis. It has a non-uniform volume charge density given in cylindrical coordinates by ρ(s) = C (s/a)^2 ,where C is a positive constant. In addition, there is a uniform volume charge density −σ on the outer cylindrical shell of radius b, where σ is a positive constant. Region 2 is a vacuum.

For parts (a) through (c), use Gauss’ Law and determine the electric fields (both magnitude and direction of the electric field) in

(a) Region 1: inside the inner cylinder (s < a)

(b) Region 2: between the inner and outer cylinders (a < s < b)

(c) Region 3: outside the outer cylinder (s > b)

(d) Is the electric field continuous at each surface? (s = a and s = b surfaces)

(e) What is the electric potential difference ∆Vab between the surface of the inner cylinder (s = a) and the surface of the outer cylinder (s = b)? Which surface has a higher potential? 1.

2) We can model the earth as a solid spherical conductor of radius RE surrounded by a concentric spherical conducting shell with inner radius Ri , and outer radius Ro, which is the ionosphere. The earth has charge +Q, while the ionosphere has zero net charge.

Write all answers in terms of Q, RE, Ri , Ro, and 0.

For parts (a) through (c), what is the surface charge density on

(a) the outer surface of the inner sphere of radius RE?

(b) the inner surface on the spherical shell at radius Ri?

(c) the outer surface of the spherical shell at radius Ro?

For parts (d) through (g), determine the electric field E(r) everywhere in space:

(d) r < RE

(e) RE < r < Ri

(f) Ri < r < Ro

(g) r > Ro

(h) Calculate the energy of the system.

(i) Determine the potential at the center given that the potential is zero at r = ∞.

(j) Find the capacitance of the earth-ionosphere system assuming that the ionosphere has net charge −Q instead of zero.

3) Two charges are on the z-axis, charge +q at z = +a and −q at z = −a. (Hint: This is NOT a continuous charge distribution but two discrete point charges.)

(a) Find the electric potential V (x, y, z) at a field point r = (x, y, z).

(b) Find the potential V (x, y, 0) at a point (x, y, 0) on the xy-plane.

(c) What is the total electrostatic energy of this system?

(d) Using the result of part (c), find out how much work it takes to move the charges closer so that their separation is a rather than 2a.

An archeological specimen containing 9.42 g of carbon has an activity of 1.58 Bq. How old (in years) is the specimen? Do not enter unit.

Givens (Questions 1

a hot reservoir at 576k transfers 2100 j of heat irreversibly to a cold reservoir at 350 k. Find change in entropy of the universe.

An airplane traveling at half the speed of sound emits a sound of frequency 5.29 kHz.

(a) At what frequency does a stationary listener hear the sound as the plane approaches? kHz

(b) At what frequency does a stationary listener hear the sound after the plane passes? kHz

The Navajo Generating Station was a 2250 MW plant when operating at full power.

a) Assuming the plant operates at 38% efficiency and that coal has a heat content of

10,500 BTU/lb, calculate how many tons of coal are used per year if the plant

operates at full capacity (assume 24 hrs/day, 7 days/week) .

b) Calculate the area needed to replace the power generated by NGS with Si

photocells operating at 21% efficiency assuming an average solar insolation of 6

kWhr/m2. show all work

Bycicles convert force into torque (pedal to axis), torque into force (axis to chain using the front gear), force into a torque (chain to back wheel using back gear), and finally, torque into force (wheel on road), and that accelerates the bike. If you make the front gear smaller, is it easier or harder to pedal (explain in terms of forces/torques)? If you make the back gear smaller, is it easier or harder to pedal?

The figure shows two parallel nonconducting rings with their central axes along a common line. Ring 1 has uniform charge q₁ and radius R; ring 2 has uniform charge q₂ and the same radius R. The rings are separated by a distance 3.00R. The ratio of the electric field magnitudes of Ring 1 and Ring 2 at point P on the common line is 1.59. What is the ratio of charge magnitudes q₁/q₂?

A bumper car with mass m₁ = 115 kg is moving to the right with a velocity of v₁ = 4.8 m/s. A second bumper car with mass m₂ = 95 kg is moving to the left with a velocity of v₂ = -3.8 m/s. The two cars have an elastic collision. Assume the surface is frictionless.

1. What is the velocity of the center of mass of the system?

2. What is the initial velocity of car 1 in the center-of-mass reference frame?

3. What is the final velocity of car 1 in the center-of-mass reference frame?

4. What is the final velocity of car 1 in the ground (original) reference frame?

5. What is the final velocity of car 2 in the ground (original) reference frame?

6. In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide.

What is the final speed of the two bumper cars after the collision?

ANSWER THIS QUESTION IN PARTICULAR PLEASE. DO NOT PROVIDE A GENERALIZED SOLUTION.

An unpolarized beam of light is incident on a pair of polarizing filters. The first filter set to polarize in the vertical direction and the second filter is set to polarize 38° from vertical. What is the intensity of the light beam after the second filter relative to the original beam?

A 679-kg elevator starts from rest and moves upward for 3.30 s with constant acceleration until it reaches its cruising speed, 1.63 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this amount of power compare with its power during an upright trip with constant speed?

Determine the number of combined states, in the form of total |s m s >, for the combination of four spin ½ particles.

Do NOT determine the coefficients in the composite states.

Hint: make two combinations of spin - ½ particles, one for spins 1 and 2, and one for spins 3 and 4, and combine those

A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -2q and the outer shell has a total charge of +4q.

Select True or False for the following statements.

The total charge on the inner surface of the small shell is zero.
True False  The total charge on the inner surface of the large shell is zero.
True False  The electric field in the region r < a is zero.
True False  The electric field in the region r > d is zero.
True False  The total charge on the outer surface of the large shell is +2q.
True False  The electric field in the region c < r < d is zero.
True False  The total charge on the outer surface of the small shell is -6q.

Smarty McGuy intends to charge the parallel plate capacitor inside his intergalactic Ford Pinto (built by Doc Dre) with a lightning strike of 26x10³ amps. Doc Dre's capacitor specifications are listed below:

The distance between the capacitor plates is 5 microns

The surface area of the capacitor plates is 3,844 cm²

There is a dielectric between the capacitor plates

What is the minimum dielectric constant of the material between the plates needed to store all the charge from the lightning assuming that the lightning strike lasts for 6x10^-6 seconds and provides 1.21 Gigawatts of power? Assume the dielectric doesn't reach its breakdown voltage.

(a) Name 4 major components of a Gamma camera. Briefly explain the function of each component.
Also, describe the advantages and disadvantages of using “thin” scintillating crystal.

(b) In an experiment with 51.80 MBq 99mTc, 5.88×105 counts are measured in 2 minutes. According to the manufacturer the sensitivity is 202 cnts/(min⋅μCi) (American manufacturers still use Ci instead of Bq, 1μCi = 37 kBq). What is the difference between the sensitivity of the measurement and the factory specification?

(c) in a NM scan, we use a specific contrast agent with half-life of 2h and emitted gamma radiation with wavelength of the 8.79x0-12 m. We image the patient immediately after the injection and the scan takes 20 minutes. Injecting 1 mCi, the acquired NM images have signal-to-noise ratio of 40. Calculate the SNR if we inject the patient with 3 mCi and scan him for 60 minutes.