Describe the principle behind the working of a motor and the generator?Then, explain the “motor- generator duality”

How do magnetic field lines from the coil compare with those of permanent magnet? Explain why they have similar shape. What are the sources of these magnetic fields?

Solve using any method you would like, but show your work. Suppose we were considering the Atwood’s machine pictured at right. A block of mass M1 = 1.5 kg is on a surface with coefficient of friction µ = 0.10, which is tilted at an angle α = 30º. A second block of mass M2 = 3.5 kg is hanging vertically. The two blocks are connected via an ideal massless string that passes over a pulley of mass mp = 0.55 kg and radius rp= 7.5 cm which can be treated as a solid disk. At time t0 block 2 is released from rest and it begins to fall.

a. Determine the magnitude of the friction force. Show your work

b. Determine the speed of the blocks when block 2 hits the floor, 0.35 m below where it starts. Show your work

c. After block 2 hits the floor, how much farther will block 1 slide up the incline before coming to rest? Show your work (hint, once block 2 hits the floor the tension in the string goes to zero – will it have any effect anymore?)

Write and explain the integral form of Maxwell’s Equations as applied to free space, that is, in the absence of any dielectric or magnetic material.

At the equator, near the surface of the Earth, the magnetic field is approximately 50 ?? northward, and the electric field is about 100 N/C downward in fair weather. Find the magnitude and direction of gravitational, electric, and magnetic forces on an proton in this environment, assuming the proton has an instantaneous velocity of 5?106m/s directed to the west.

For the thermal radiation from an ideal blackbody radiator with a surface temperature of 2100 K, let Ic represent the intensity per unit wavelength according to the classical expression for the spectral radiancy and Ip represent the corresponding intensity per unit wavelength according to the Planck expression. What is the ratio Ic/Ip for a wavelength of (a) 400 nm (at the blue end of the visible spectrum) and (b) 210 μm (in the far infrared)? (c) Does the classical expression agree with the Planck expression in the shorter wavelength range or the longer wavelength range?

1. A particle in the infinite square well (width a) starts out being equally likely to be found in the first and last third of the well and zero in the middle third.
   1. What is the initial (t=0) wave function? Find A and graph the initial wave function.
   2. What is the expectation value of x? Show your calculation for the expectation value of x, but then say why you could have just written down the answer. Will you ever find the particle at the expectation value of x at t = 0?
   3. What is the probability of finding the first four stationary states?

In the figure, block 2 of mass 2.90 kg oscillates on the end of a spring in SHM with a period of 26.00 ms. The position of the block is given by x = (0.700 cm) cos(?t + ?/2). Block 1 of mass 5.80 kg slides toward block 2 with a velocity of magnitude 8.70 m/s, directed along the spring's length. The two blocks undergo a completely inelastic collision at time t = 6.50 ms. (The duration of the collision is much less than the period of motion.) What is the amplitude of the SHM after the collision?

Two 1.9 kg balls are attached to the ends of a thin rod of negligible mass, 62 cm in length. The rod is free to rotate in a vertical plane about a horizontal axis through its center. With the rod initially horizontal as shown, a 0.42 kg wad of wet putty drops onto one of the balls with a speed of 3.2 m/sec and sticks to it.

1)

What is the ratio of the magnitude of angular momentum of the entire system just after the collision to just before the collision? (|L|_after/|L|_before)

2)

What is the angular speed of the system just after the putty wad hits?

rad/sec

3)

What is the ratio of the kinetic energy of the entire system just after the collision to just before the collision? (KE_after/KE_before)

4)

Through what angle will the system rotate until it momentarily stops?

Two long, straight wires are perpendicular to the plane of the paper and at a distance 0.2 m from each other, as shown in the figure. The wires carry currents of I1 = 2.6 A and I2 = 5 A in the direction indicated (out of the page). Find the magnitude and direction of the magnetic field (in µT) at a point A midway between the wires. You need to indicate the direction with a positive or a negative value for the magnetic field. Keep in mind that a vector is positive if directed to the right and negative if directed to the left on the x axis and it is positive if directed up and negative if directed down on the y axis. Your answer should be a number with two decimal places, do not include the unit.

Consider the Potential V(r) =Vo (c/r) exp (-r/c) (where c is a constant) and a deutron of reduced mass m moving in this potential . (a) Using a trial wave function R(r) = exp (- d *r / c) (d is constant ) find the ground state energy if Vo= 1.35 (b) If one bound state energy is -2.2 find Vo

There are four charges, each with a magnitude of 2.16

A long straight cable of radius a = 0.100 m lies along the x-axis. Inside the cable the current density is constant and has magnitude J = 5.00 ( Ampere m^-2 ). The current density is directed along the + x direction. Let s be cylindrical radius.

i. What is the current running through the cable between radius 0 and s?

ii. What is the magnetic field as a function of s inside the cable?

iii. What is the total current running through the cable?

iv. What is the magnetic field as a function of s outside the cable?