Submission deadline is April 15th.
|
Classical Mechanics |
Hall of Fame |
|---|---|
|
|
|
A smooth, conical surface is fixed, with its symmetry axis vertical, as shown in the Figure. A small pebble slides without friction inside the cone. Points A and B are the highest and lowest points of its trajectory. The magnitude of the vertical component of the pebble's acceleration at point B is six times greater than that at point A. Find the ratio hA/hB.
|
Electricity and Magnetism |
Hall of Fame |
|---|---|
|
Capacitor 2 is a parallel-plate capacitor that consists of two identical parallel plates of elliptical shape. The semi-minor and semi-major axes of this ellipse are a and b. The plate separation is d=b-a (d≪a,b). A charge Q (of the same magnitude as on the inner sphere in Capacitor 1) is placed on one plate of this capacitor, while the other plate is left uncharged. Now the two plates of both capacitors are connected via identical resistors. 1) How will the charge be distributed between the plates of each capacitor after a sufficiently long time? 2)In which capacitor is the net heat generated at the resistor greater? 3)In which capacitor will the charge transfer occur faster?
Winning entries will contain correct answers to all three questions with valid solutions. |
|
This problem deals with two capacitors of different designs. Capacitor 1 consists of two concentric spheres (see the Figure). A charge Q is placed on the inner sphere of radius a, while the outer sphere is left uncharged.
