Show that the reciprocal space of the BCC lattice forms an FCC lattice.
(Please explain every step)

In the famous Millikan oil-drop experiment, tiny spherical droplets of oil are sprayed into a uniform vertical electric field. The drops get a very small charge (just a few electrons) due to friction with the atomizer as they are sprayed. The field is adjusted until the drop (which is viewed through a small telescope) is just balanced against gravity, and therefore remains stationary. Using the measured value of the electric field, we can calculate the charge on the drop and from this calculate the charge e of the electron. In one apparatus, the drops are 1.40 mm in diameter and the oil has a density of 0.850 g/cm³.

a) If the drops are negatively charged, which way should the electric field point to hold them stationary? Up or down? Please explain your reasoning. (1)

b) If a certain drop contains four excess electrons, what magnitude electric field is needed to hold it stationary? Please express your answer to three significant figures. (2)

c) If you measure a balancing field of 5183 N/C for another drop. How many excess electrons are on this drop? Please express your answer as an integer. (2)

A golf ball hit from the tee at ground level lands 62 m ahead 3.0 s later. What was the initial speed of the ball and at what angle with the horizontal did it come out?

Three point charges are on the x-axis: q1 at the origin, q2 at 3 m, and q3 at 7 m.

A) Find the potential at the point (0, 4 m) if q1 = q2 = q3 = 2 µC. The Coulomb constant is 8.99 × 109 N · m2 /C 2 Answer in units of kV.

B) Find the potential at the point (0, 4 m) if q1 = q2 = 2 µC and q3 = −2 µC . Answer in units of kV.

C) Find the potential at the point (0, 4 m) if q1 = q3 = 2 µC and q2 = −2 µC . Answer in units of kV.

A vertical infinite wire along the z-axis has two symmetries: One is a rotational symmetry around the z-axis while the other is a translational symmetry along the z-axis. Describe the symmetries of a) a sphere, b) an infinite plane, c) a circular plate, d) a finite length rod with circular cross section, and e) a finite length bar with a square cross section.

Please explain process.

The mass of the sun is 2*1030 kg. It currently consists to about 70% (mass) of hydrogen. The dominant source of energy for the sun is the pp-chain (type I) fusion process in which four protons fuse into a 4He core consisting of two protons and two neutrons. This process releases 26.22 MeV ( = 4.2*10-12 J) of energy. Assume that to first order the luminosity of the sun remains constant at 1.1 times its current-day value. How long will it take for the sun until the fraction of hydrogen is reduced from 70% to 30%?

a- Consider an electron that moves freely in metal and a particle moves freely in vacuum. Briefly explain differences between the energy of these particles. b- Briefly explain the temperature dependent conductivity of metal, semiconductor and insulator. (Please write your answer by asking your self “How and Why change” questions )

3. An inductor/resistor circuit is powered by a direct current EMF of 3.00 V until the inductor is fully powered. The decay coefficient of the circuit is 2.15 ms. The inductor has a value of 140 mH.

a) After the EMF is turned off, how long does it take the current in the circuit to drop from a max of 46.2 mA to 11.5 mA?

b) What is the value of the resistor?

c) If the inductor has a length of 0.75 cm and 3000 loops, what is its cross sectional area?

A vertical glass tube of length L = 1.280000 m is half filled with a liquid at 20.000 000 degrees C. How much will the height of the liquid column change when the tube and liquid are heated to 30.000000 degrees C? Use coefficients alpha_glass = 1.000 000 x 10^-5/K and Beta_liquid = 4.000 000 x 10^-5/K

A glass rod is rubbed on a silk cloth, and then separated
from each other. When the rod and the silk cloth are
separated by 35 cm, a force of magnitude 2.20x10^−21 N is
measured between the rod and cloth.
a) Calculate the total charge on the glass rod.
b) Calculate the total charge on the silk cloth.
c) How many electrons were transferred from the glass rod to the silk cloth.
d) Explain why a material like copper is a good conductor of electricity, while a material like wood is a poor
conductor of electricity.

One particle has a mass of 3.84 x 10-3 kg and a charge of +8.90 μC. A second particle has a mass of 8.33 x 10-3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.158 m, the speed of the 3.84 x 10-3 kg-particle is 190 m/s. Find the initial separation between the particles.

A block of mass m = 3.50 kg is released from rest from point A and slides on the frictionless track shown in the figure below. (Let h_a = 5.20 m.)

(a) Determine the block's speed at points B and C

(b) Determine the net work done by the gravitational force on the block as it moves from point A to point C.
J

A red ball is thrown down with an initial speed of 1.4 m/s from a height of 29 meters above the ground. Then, 0.6 seconds after the red ball is thrown, a blue ball is thrown upward with an initial speed of 25.6 m/s, from a height of 1 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s².

1)

What is the speed of the red ball right before it hits the ground?

m/s

2)

How long does it take the red ball to reach the ground?

s

3)

What is the maximum height the blue ball reaches?

m

4)

What is the height of the blue ball 1.8 seconds after the red ball is thrown?

m

5)

How long after the red ball is thrown are the two balls in the air at the same height?

s

A particle moves in the xy plane with constant acceleration. At t = 0 the particle is at vector r1 = (3.6 m)i + (2.8 m)j, with velocity vector v1. At t = 3 s, the particle has moved to vector r2 = (11 m)i − (1.8 m)j and its velocity has changed to vector v2 = (4.6 m/s)i − (6.7 m/s)j. (a) Find vector v1. vector v1 = m/s

(b) What is the acceleration of the particle? vector a = m/s2

(c) What is the velocity of the particle as a function of time? vector v(t) = m/s

(d) What is the position vector of the particle as a function of time? vector r(t) = m