Calculating Flux for Hemispheres of Different Radii

# Calculating Flux for Hemispheres of Different Radii -...

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Calculating Flux for Hemispheres of Different Radii Learning Goal: 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): , where is the flux through a surface with differential area element , and is the electric field in which the surface lies. There are several important points to consider in this expression: 1. It is an integral over a surface, involving the electric field at the surface. 2. 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. 3. The scalar (dot) product implies that only the component of normal to the surface contributes to the integral. That is, , where is the angle between and . When you compute flux, try to pick a surface that is either parallel or perpendicular to , so that the dot product is easy to compute. Two hemispherical surfaces, 1 and 2, of respective radii and , are centered at a point charge and are facing

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Calculating Flux for Hemispheres of Different Radii each other so that their edges define an annular ring (surface 3), as shown. The field at position due to the point charge is: where is a constant proportional to the charge, , and is the unit vector in the radial direction. Part A What is the electric flux through the annular ring, surface 3? Hint A.1 Apply the definition of electric flux Hint not displayed Express your answer in terms of , , , and any constants. ANSWER: = 0 Correct Part B What is the electric flux through surface 1? Hint B.1 Apply the definition of electric flux Hint not displayed Hint B.2 Find the area of surface 1 Hint not displayed Express in terms of , , , and any needed constants. ANSWER:
Calculating Flux for Hemispheres of Different Radii Part A = Correct Part C What is the electric flux passing outward through surface 2? Hint C.1 Apply the definition of electric flux Hint not displayed Hint C.2 Find the area of surface 2 Hint not displayed Express in terms of , , , and any constants or other known quantities. ANSWER: = Correct Observe that the electric flux through surface 1 is the same as that through surface 2, despite the fact that surface 2 has a larger area. If you think in terms of field lines, this means that there is the same number of field lines passing through both surfaces. This is because of the inverse square, , behavior of the electric field surrounding a point particle. A good rule of thumb is that the flux through a surface is proportional to the number of field lines that pass through the surface.

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Gauss's Law Learning Goal: To understand the meaning of the variables in Gauss's law, and the conditions under which the law is applicable. Gauss's law is usually written
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## This note was uploaded on 04/09/2010 for the course PHYS 1010 taught by Professor Thompson during the Spring '07 term at New York Medical College.

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Calculating Flux for Hemispheres of Different Radii -...

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