Part a What is the electric flux Φ3 through the annular ring, surface 3? Express your answer in terms of C, r1, r2, and any constants

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Part a What is the electric flux Φ3 through the annular ring, surface 3? Express your answer in terms of C, r1, r2, and any constants.

part b What is the electric flux Φ1 through surface 1? Express Φ1 in terms of C, r1, r2, and any needed constants.

part c What is the electric flux Φ2 passing outward through surface 2? Express Φ2 in terms of r1, r2, C, and any constants or other known quantities.

Part C What is the electric flux ?2 passing outward through surface 2? Express ?2 in terms of r1, r2, C, and any constants or other known quantitie View Available Hint(s) 2 Submit
Two hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are centered at a point charge and are facing each other so that their edges define an annular ring (surface 3), as shown. The field at position due to the point charge is Part A what is the electric flux ?? through the annular ring, surface 3? Express your answer in terms of C, r1, r2, and any constants. where C is a constant proportional to the charge, F, and /r is the unit vector in the radial direction. View Available Hint(s) igure 1 of 1 surface 2 surface 2 Submit surface 3 surface 3 Part B E ficl surface 1 what is the electric flux ? through surface 1 ? Express ?1 in terms of C, r, r2, and any needed constants. surface 1 View Available Hint(s) Side View Front Vievw

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): ΦE=∫E? ⋅dA? , where ΦEis the flux through a surface with differential area element dA? , and E?  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.

dA?  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 E? ⋅dA?  implies that only the component of E?  normal to the surface contributes to the integral. That is, E? ⋅dA? =??E? ????dA? ??cos(θ), where θ is the angle between E?  and dA? .

When you compute flux, try to pick a surface that is either parallel or perpendicular to E? , so that the dot product is easy to compute.

(Figure 1)

Two hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are centered at a point charge and are facing each other so that their edges define an annular ring (surface 3), as shown. The field at position r?  due to the point charge is:

E? (r? )=Cr2r^

where C is a constant proportional to the charge, r=??r? ??, and r^=r? /r is the unit vector in the radial direction.