A cube has sides of length L = 1.00 mm. One corner is at the origin. The nonuniform electric
field is given by E~ = (19.00N/C ·m) x ˆi−(1.34N/C ·m) z
ˆk. (a) find the electric flux through
each of the six cube faces S1, S2, S3, S4, S5, S6. (b) Find the total electric charge inside the
cube.

A wire containing a charge of λ Coulombs per unit length is embedded along the axis of a cylinder of dielectric material. There is no free charge inside the dielectric. The composition of the dielectric is non-uniform, such that its permittivity is a function of the distance from the central axis, i.e. ε = ε(r).

(a) Find the displacement field, D as a function of distance from the central axis of the wire, r.

(b) if the electric field strength, E, is independent of r, determine the form of ε(r).

(c) Find an expression for the electrostatic potential as a function of r.

A 7.2 kg block with a speed of 10 m/s collides with a 19 kg block that has a speed of 5.4 m/s in the same direction. After the collision, the 19 kg block is observed to be traveling in the original direction with a speed of 5.4 m/s. (a) What is the velocity of the 7.2 kg block immediately after the collision?(b) By how much does the total kinetic energy of the system of two blocks change because of the collision? (c) Suppose, instead, that the 19 kg block ends up with a speed of 4.7 m/s. What then is the change in the total kinetic energy?

Robot No. 5 (mass 273kg) and Prisoner No. 6 (mass 66kg) stand on a frictionless ice rink, both holding a rope. The robot is at x = −3m and the prisoner is at x = 17m. The robot starts winding up the rope. Considering the two of them plus the rope as a system, there are no external horizontal forces on either of them. When the rope is fully wound, where do No. 5 and No. 6 meet?

Problem 3: Double-slit experiment The monochromatic light diffracts on the two slits which are 0.1 mm apart (their size is negligible) and produces an interference pattern on the wall which is 3 m far from the apparatus.

a) The distance between the central bright fringe and the first off-center bright fringe is 2 cm. What is the wavelength of the light? Which color is it?

b) How many bright and dark fringes could we see on the wall?

c) We change the film with slits and the distance between adjacent dark fringe and bright fringe is 7 mm. What is the distance between two slits now?

Two identical probes are sent along the same path toward a neutron star. A neutron star is very dense, packing as much as 2 solar masses2 solar masses into a sphere with a radius on the order of 10 km. At the moment shown, the two probes are d=55.3 kmd=55.3 km and D=178 kmD=178 km away from the center of the neutron star, respectively.

Find the distance between the center of mass of the two probe system and its center of gravity.

ESSAY QUESTIONS 8 Define the concepts of energy, work and power and explain how they are related. Provide an example of a conceptual physics problem that might involve all three factors.

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +9q. Sphere B carries a charge of -q. Sphere C carries no net charge. Spheres A and B are touched together and then separated. Sphere C is then touched to sphere A and separated from it. Lastly, sphere C is touched to sphere B and separated from it. (a) What is the ratio of the final charge on sphere C to q? What is the ratio of the final total charge on the three spheres to q (b) before they are allowed to touch each other and (c) after they have touched?

Two football players collided on the field, and both went flying backwards. Energy was transferred from each player to the other, sending them in the opposite direction from which they had been running.

tell whether elastic or inelastic?

explain how energy was conserved/not conserved

describe all forms of energy incolved and how energy was transferred between them

describe the work done on the sytem, including its sign and source

Two capacitors C₁ = 5.1 ?F, C₂ = 19.8 ?F are charged individually to V₁ = 14.9 V, V₂ = 3.4 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.

Calculate the final potential difference across the plates of the capacitors once they are connected.

C) By how much (absolute value) is the total stored energy reduced when the two capacitors are connected?

Part a is 5.76V

Part b is 4.66E-5 C

Please help me with part c! In J please

Please answer in detail the discussions questions below.

1. Why do optical fibers have a minimum bend radius? What might happen if this minimum bend radius is exceeded?

2. Find or create your own application for the color dependence of the index of refraction. Your example need not be fully developed, but it should (1) address some task, and (2) be clear about the application of the color dependence to the task.

.How does the velocity of air moving over the top of the wing of an airplane in flight compare to the velocity of air moving under the wing. explain the answer using Bernoulli's principle.

A woman is riding a Jet Ski at a speed of 30 m/s and notices a seawall straight ahead. The farthest she can lean the craft in order to make a turn is 23

Tarzan has foolishly gotten himself into another scrape with the animals and must be rescued once again by Jane. The 60.0 kg Jane starts from rest at a height of 5.50 m in the trees and swings down to the ground using a thin, but very rigid, 32.0 kg vine 8.50 m long. She arrives just in time to snatch the 72.0 kg Tarzan from the jaws of an angry hippopotamus. What is Jane's (and the vine's) angular speedHow high will Tarzan and Jane go on their first swing after this daring rescue?

A 25 g glass tumbler contains 200 mL of water at 24°C. If two 15 g ice cubes each at a temperature of -3°C are dropped into the tumbler, what is the final temperature of the drink? Neglect thermal conduction between the tumbler and the room. 1°C