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)?

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.)

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