Consider a point charge q in three-dimensional space. Symmetry requires the electric field to point directly away from the charge in all directions. To find E(r), the magnitude of the field at distance r from the charge, the logical Gaussian surface is a sphere centered at the charge. The electric field is normal to this surface, so the dot product of the electric field and an infinitesimal surface element involves cos⁡(0)=1. The flux integral is therefore reduced to ∫E(r)dA=E(r)A(r), where E(r) is the magnitude of the electric field on the Gaussian surface, and A(r) is the area of the surface.

Determine the magnitude E(r) by applying Gauss's law.

Write the equation for momentum, first using symbols for the variables, then using words for the variables.

Unpolarized light whose intensity is 1.19 w/ is incident on a polarizer. (a) what is the intensity of the light leaving the polarizer? (b) if the analyzer is set at an angle of = 41.0∘ with respect to the polarizer, what is the intensity of the light that reaches the photocell?

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?