1. An observer moving at a speed of 0.995c relative to a rod (see figure below) measures its length to be 2.50 m and sees its length to be oriented at 29.00° with respect to the direction of motion.
(a) What is the proper length of the rod?
(b) What is the orientation angle in a reference frame moving with the rod?
2. In a Young's interference experiment, the two slits are separated by 0.17 mm and the incident light includes two wavelengths: λ1 = 540 nm (green) and λ2 = 450 nm (blue). The overlapping interference patterns are observed on a screen 1.38 m from the slits.
(a) Find a relationship between the orders m1 and m2 that determines where a bright fringe of the green light coincides with a bright fringe of the blue light. (The order m1 is associated with λ1, and m2 is associated with λ2.)
(b) Find the minimum values of m1 and m2 such that the overlapping of the bright fringes will occur and find the position of the overlap on the screen.
3. The work function for silver is 4.26 eV.
(a) Convert the value of the work function from electron volts to joules.
(b) Find the cutoff frequency for silver.
(c) What maximum wavelength of light incident on silver releases photoelectrons from the silver's surface?
(d) If light of energy 8.6 eV is incident on silver, what is the maximum kinetic energy of the ejected photoelectrons? Give the answer in electron volts.
(e) For photons of energy 8.6 eV, what stopping potential would be required to arrest the current of photoelectrons?
4. Show (by calculating the velocity in terms of c) that if an electron were confined inside an atomic nucleus of diameter 2.4 10-15 m, it would have to be moving relativistically, whereas a proton confined to the same nucleus can be moving at less than one-tenth the speed of light. (Give all answers to 4 decimal places.)
(a) When the confined particle is an electron, ER = 0.511 MeV.
(b) When the confined particle is a proton, ER = 939 MeV.
6. A hydrogen atom is in its third excited state (n = 4). Using the Bohr theory of the atom, calculate the following.
(a) the radius of the orbit
(b) the linear momentum of the electron
(c) the angular momentum of the electron
(d) the kinetic energy
(e) the potential energy
(f) the total energy
7. Three point charges are located at the corners of an equilateral triangle. Find the magnitude and direction of the net electric force on the 1.80 µC charge. (A = 1.80 µC, B = 6.50 µC, and C = -3.80 µC.)
counterclockwise from the +x-axis
8. Two point charges lie along the y-axis. A charge of q1 = -7.5 μC is at y = 6.0 m, and a charge of q2 = -8.5 μC is at y = -4.0 m. Locate the point (other than infinity) at which the total electric field is zero.
9. The resistor R dissipates 16 W of power. Determine the possible values of R. (ΔV = 73 V)
10. Three long, parallel conductors carry currents of I = 3.0 A. The figure below is an end view of the conductors, with each current coming out of the page.
Given that a = 1.6 cm, determine the magnitude and direction of the magnetic field at each of the following points:
(a) point A
(b) point B
(c) point C
11. A series circuit contains a 3.00 H inductor, a 3.80 µF capacitor, and a 25.0 resistor connected to a 120 V (rms) source of variable frequency. Find the power delivered to the circuit when the frequency of the source is each of the following:
(a) the resonance frequency
(b) one-half the resonance frequency
(c) one-fourth the resonance frequency
(d) two times the resonance frequency
(e) four times the resonance frequency