To understand the definition of electric flux, and how to calculate it. flux is the amount of a vector field that "flows" through a surface. we now discuss the electric flux through a surface (a quantity needed in gauss's law): φe=∫e⃗ ⋅da⃗ , where φe is the flux through a surface with differential area element da⃗ , and e⃗ is the electric field in which the surface lies. there are several important points to consider in this expression: it is an integral over a surface, involving the electric field at the surface. da⃗ is a vector with magnitude equal to the area of an infinitesmal surface element and pointing in a direction normal (and usually outward) to the infinitesmal surface element. the scalar (dot) product e⃗ ⋅da⃗ implies that only the component of e⃗ normal to the surface contributes to the integral. that is, e⃗ ⋅da⃗ =∣∣e⃗ ∣∣∣∣da⃗ ∣∣cos(θ), where θ is the angle between e⃗ and da⃗ .

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?