A long, hollow cylinder with inner radius R1 and outer radius R2 carries current along its length. The current is uniformly distributed over the cross-sectional area of the cylinder and has current density J. 1. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points inside the hollow interior (r 2. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points inside the solid conductor (R1 3. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points outside the conductor (r>R2).

Now that the first three steps have been explained, identify the next three steps, in order. calculate the magnitude of r sum vector components calculate a and b magnitudes calculate the direction of r, calculate x,y components step 4 step 5 step 6

The of a machine determines its "usefulness." a. input force b. output force c. mechanical advantage

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)