A steady current I flows through a wire of radius a. The current density in a wire varies with r as J = kr2, where k is a constant and r is the distance from the axis of the wire. Find expressions for the magnitudes of the magnetic field inside and outside the wire as a function of r. (Hint: Find the current through an Ampèrian loop of radius r using Ithru = J · dA. Use the following as necessary: μ0, a, I and r. Do not substitute numerical values; use variables only.) Binside = u0·I·r2 2·π·a3 Boutside = u0·I 2·π·r

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

Two polarizers are oriented at 70∘∘ to one another. unpolarized light falls on them. what fraction of the light intensity is transmitted?

What type of relationship exists between the length of a wire and the resistance, if all other factors remain the same? o a. resistance is directly related to length. ob. resistance is directly related to the square of the length. c. resistance is inversely related to the length. d. resistance is inversely related to the square of the length. reset next