A 100 meter long wire carrying a current of .4 amps into the board is at (-5, 0) meters and another 100-m long wire carrying a current of .6 amps out of the board is at (+3, 0) meters.

a) Find the Magnetic Force between these charges.

b) Where can a third wire be placed so that it experiences no force? Where can it be placed on the x-axis so it experiences a force of magnitude 5 μN (the wire has a current of .5 amps out of the board and is 100-m long)?

c) What is the total force (magnitude and direction) on a 100-m long wire placed at (-2, 4) meters which carries a current of .5 amps out of the board? What is the total magnetic field (magnitude and direction) at that location?

Answers Should Be:

a) F = .6 μN repulsive

b) (-21, 0) meters for 0 force,

(-4.035, 0) m & (1.635, 0) m & (-5.703, 0) m & (4.103, 0) m for 5 μΝ

c) F = 1.21 μN, θ = 2.58^o above the x-axis

B = 24.2 nT, θ = 87.42^o below the x-axis

In the single electron transistor, to achieve Coulomb blockade, it is necessary that the tunnel barrier of the system is much higher than the quantum resistance Rt. Calculate Rt

describe and differentiate chemical, mechanical, gravitational, elastic, nuclear, electrical, radiant and thermal energies

Explain the ultraviolet catastrophe. Discuss the conclusions obtained from Planck’s formula under the conditions of short and long wavelength.

Consider a system composed of four harmonic oscillators. The energy of the ground state is E0/2. The distribution of oscillators in each system is described by the set following distributions {Ni} 

Distribution I: N0=2, N1=1 N2=1, N3=0 

Distribution II: N0=1, N1=3 N2=N3=0 

Distribution III: N0=3 N1=N2=0 N3=1

For each distribution, calculate.

1. The energy of each system and the average energy

2. The number of equivalent particle arrangements W that yield equivalent distributions (assume the particles are distinguishable), or degeneracy, of each distribution

3. The absolute entropy S of each distribution; which distribution is the most likely to occur?

4. Do any of these distributions correspond to thermodynamic equilibrium? If not, state the condition for thermodynamic equilibrium

- Consider three distributions described by the set of energy level number populations {Ni}

System I Distribution: N0=1, N1=N2=2, N3=0

System II Distribution: N0=N1=N2=1, N3=2

System III Distribution: N0=N2=N3=0, N1=5

Which distribution is the most likely to occur? Explain why, by calculating the degeneracy of each distribution (assume the particles are distinguishable) and the absolute entropy S.

An electron has a non-relativistic speed of v=1.5×10^5 m / s. Determine:

A) Its de Broglie wavelength.

B) Its kinetic energy.

C) The resting energy of the electron in joules and in electron volts.

d) What is the speed of the electron if the relativistic kinetic energy is equal to the rest energy?

e) The momentum of the electron at a speed of 0.80c.

f) The de Broglie wavelength for electron with a speed of 0.80c.

A bus driver heads south with a steady speed of v1 = 20.0 m/s for t1 = 3.00 min, then makes a right turn and travels at v2 = 25.0 m/s for t2 = 2.60 min, and then drives northwest at v3 = 30.0 m/s for t3 = 1.00 min. For this 6.60-min trip, calculate the following. Assume +x is in the eastward direction.

(a) total vector displacement (Enter the magnitude in m and the direction in degrees south of west.)

magnitude = ? And direction =?

(b) average speed (in m/s)

(c) average velocity (Enter the magnitude in m/s and the direction in degrees south of west.)

magnitude = ? And direction =?

For each of the following processes, describe what kind of energy is being converted into what other kind(s). Valid forms of energy for the purpose of this question are “kinetic energy of (object),” “gravitational potential energy,” “elastic potential energy of (object),” or “internal energy of (object).” There may be more than one conversion involved, so your answer should be a kind of narration of the energy conversion(s).

For example, if the process is, “A girl skating on rollerblades skids to a halt,” then your answer should read something like: The kinetic energy of the girl is converted into internal energy of the skates and of the road.

You drop a book, and it falls to the floor and lands with a thud.

You drop a rubber ball, which hits the floor and rebounds back up to your hand. (Hint: Think about what happens to the ball while it is in contact with the floor.)

You pour milk from a carton into a drinking glass.

You pick up a heavy box from the floor and lift it onto a table.

You stretch a rubber band between your thumb and forefinger and release the rubber band. The rubber band shoots straight up into the air, falls back down, and lands motionless on the ground.

Two charges, 12 mC and 11 mC, are fixed in place 1.0 m apart, with the second one to the right. Find the magnitude and direction of the net force on a -2.0 nC charge, placed at the following locations:

a) halfway between the two: |F|=

b) b) half a meter to the left of the 12 mC charge: |F|=

In each of the following cases, predict the sign of change in entropy by providing proper explanation.                                                                                                                                                            (i) Isothermal expansion.


      (ii) Liquefaction of a gas

The collisional diameter d of a H2 molecule is about 0.25 nm=2.5×10?10m. For H2 gas at 0?C and 1 bar, calculate the following:

Part A

the root-mean-square velocity.

Express your answer using three significant figures and include the appropriate units.

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Part B

the translational kinetic energy of 1 mol of H2 molecules.

Express your answer using three significant figures and include the appropriate units.

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Part C

the number of H2 molecules in 1 mL of the gas.

Express your answer using three significant figures.

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Part D

the mean free path.

Express your answer using two significant figures and include the appropriate units.

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Part E

the number of collisions each H2 molecule undergoes in 1 s.

Express your answer using two significant figures.

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Part F

the total number of intermolecular collisions in 1 s in 1 mL of the gas.

Express your answer using two significant figures.

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A catfish is 2.00 m below the surface of a smooth lake. (a) What is the diameter of the circle on the surface through which the fish can see the world outside the water? (b) If the fish descends, does the diameter of the circle increase, decrease, or remain the same?