Consider the following instantaneous representation of a standing wave: ex = v3e, sin(bz) cos(wt), hy = -v3 cos(bz) sin(wt). as a function of z: a) calculate the instantaneous electric field energy density. [2 points] b) calculate the instantaneous magnetic field energy density. [2 points] c) what is the relationship between the instantaneous electric field energy density and the instantaneous magnetic field energy density? explain your answer. [2 points) d) calculate the instantaneous poynting vector. [2 points] e) calculate the instantaneous energy velocity. (use dimensional analysis to assist you in obtaining this expression if you do not remember it.)

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?