22. What are the two basic postulates through which Einstein based his Special Theory of Relativity on (10 points)?

21. A current I is running uniformly toward the positive z direction on a long thin plate lying on the x-z plane with wider width w. Find out the magnetic field at a place very close to the center part of the plate (3 points). If this plate is bent to form a cylinder centering at the z axis with radius r = w/2π, what will be the magnetic field inside and outside this cylinder (3 points)? What is the pressure acting on this cylinder due to the magnetic force induced by the parallel current (4 points)?

8. A torsional pendulum consists of a solid disk (mass = 2.0 kg, radius = 1.0 m) suspended by a wire attached to a rigid support. The body oscillates about the support wire. If the torsion constant is 16 N·m/rad. What is the angular frequency (in rad/s)?

7. A straight wire of length L carries a current I in the positive z direction in a region where the magnetic field is uniform and specified by Bx = 3B, By = −2B, and Bz = B, where B is a constant. What is the magnitude of the magnetic force on the wire?

6. A high-voltage transmission line carries 1000 A at 700 kV for a distance of 100 miles. If the resistance per length in the wire is 0.5 Ω/mile, what is the power loss due to resistive losses?

5. A solar cell has a light-gathering area of 10 cm² and produces 0.2 A at 0.8 V (DC) when illuminated with S = 1000 W/m² sunlight. What is the efficiency of the solar cell?

 4. An electron is accelerated through a potential difference of 25000 V. What is the de Broglie wavelength of the electron (in m)?

 3. When 1.0 gram of hydrogen combines with 8.0 grams of oxygen, 9.0 grams of water is formed. But is this true? During the reaction 2.86 × 10⁵ J of energy is released. How much mass is actually lost in this reaction?

2. Rubidium (Z = 37) and potassium (Z = 19) are similar to sodium in that they have ____ electron(s) in the outermost shell.

 1. During the volcanic eruption of Mt. Pelee in 1902, an incredibly hot "burning cloud" rolled down the mountain and incinerated the town of Saint-Pierre. From the damage done, the temperature in the cloud was estimated at 700°C. If the air temperature was 20°C and a mole of air is 29 grams, estimate the molecular weight of the gas in the "burning cloud" that made it heavier than the surrounding air. (As a follow-on, estimate the most probable composition of the cloud. Some typical volcanic gases are H₂S, SO₂, H₂SO₄, CO₂, NO.)

8. A hoop, a solid cylinder, and a solid sphere all have the same mass m and the same radius R. Each is mounted to oscillate about an axis a distance 0.5R from the center. The axis is perpendicular to the circular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below. Which is the correct ranking in order of increasing angular frequency ω (from highest to lowest)?

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