Emf

A device called a homopolar generator has a metal disk that rotates in the presence of a magnetic field perpendicular tot he disk. Sliding contacts connect the axle and the outer surface of the disk to an external circuit. a) Explain why this device produces an emf between two contacts. Is this emf oscillating or constant? b)Determine the magnitude of this emf in terms of the disks's radius R, the magnetic field strength B, and the angular rate of rotation w. (Hint: divide the dist up into rings of infinitesimal thickness dr, compute the emf created across each ring, then sum.)

Problem 3

Consider a generator. The loop in this generator rotates at an angular rate of w. The slip rings in this design ensure that the same leg of rotating loop is always connected to the same output terminal. Show that the potential difference between the output terminal is given by E=Eo cos(theta) (where theta =wt is the angle that the plane of theloop makes with the magnetic field direction at time t), and determine xin terms of the loops Length L, width W, the magnetic field strength B, and the loops angular rotation rate w .

Magnetism

A copper sulfate solution is placed in a container that contains coaxial cylindrical copper electrodes, as indicated in the picture. An electric field is created by connecting a battery across the electrodes as shown. A magnet field is created by immersing a magnet in the center of the solution as shown. Uncharged pollen grains are sprinkled in the area between the electrodes. They are observed to circulate counterclockwise when viewed from above. You hypothesize that they are carried along by the circulation of ions in the solution due to the electric and magnetic forces that act on those ions. Can you tell if the charge on the circulating ions is positive or negative? Explain.

Magnetism

A metal bar of mass m and length L slides without friction but with good electrical contact between two vertical metal posts. The bar and posts have negligible resistance. The posts are connected at the bottom by a resistor R. Assume the bar falls at constant speed v, and that there is a magnetic field coming out of the page. (a) Calculate the current flowing through the resistor. (b) Clearly show the surface charge distribution on the entire circuit (both sign and gradient). Explain how that surface charge distribution causes a current to flow in the circuit. (c) How can the speed of the bar be constant if it is falling? Calculate the speed v.

Amplitude

1. The speed of sound waves in water (density 1.00 x 10 3 kg/m 3 ) is c=1480 m/s. [2] (a) What is the average intensity (in W/m 2 ) of a 1000 Hz sound wave in water if the displacement amplitude of the wave is 1.00 nm? (1 nm=10 -9 m). [2] (b) What is the ratio of pressure amplitude to displacement amplitude in this wave? [2] (c) Assuming an absorption coefficient of 0.0001 dB/m in the water, how far does a plane wave have to travel in the water so that its displacement amplitude is reduced from 1.0nm to 0.1 nm?