part a What is the electrical flux Φ3 with theannular ring, surface ar 3? Express your answer in termsof C, r1, r2,and any constants.

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part b What is the electric flux Φ1 throughsurface1? Express Φ1 intermsof C, r1, r2,and any type of needed constants.

part c What is the electric flux Φ2 passingoutward v surface2? Express Φ2 intermsof r1, r2, C,and any type of constants or other well-known quantities.


Learning Goal:

To recognize the definition of electric flux, and also how tocalculate it.

Flux is the quantity of a vector ar that \"flows\" with asurface. We now comment on the electrical flux with a surface ar (aquantity required in Gauss\"slaw): ΦE=∫E⃗ ⋅dA⃗ ,where ΦEis the flux v a surface withdifferential area aspect dA⃗ ,and E⃗ is the electrical field in which thesurface lies. There room several essential points to think about inthis expression:

It is one integral end a surface, entailing the electrical fieldat the surface.

dA⃗ is a vector with magnitudeequal come the area of one infinitesmal surface ar element and also pointingin a direction common (and usually outward) come the infinitesmalsurface element.

The scalar (dot)product E⃗ ⋅dA⃗ impliesthat just the componentof Enormal come the surfacecontributes come the integral. Thatis, E⃗ ⋅dA⃗ =∣∣E⃗ ∣∣∣∣dA⃗ ∣∣cos(θ),where θ is the anglebetween E⃗ and also dA⃗ .

When girlfriend compute flux, try to pick a surface that is eitherparallel or perpendicular come E⃗ , so the thedot product is straightforward to compute.

(Figure 1)

Two hemispherical surfaces, 1 and also 2, of respectiveradii r1 and also r2, are centered at apoint charge and are encountering each various other so the their edge definean annular ring (surface 3), as shown. The ar atposition r⃗ due to the suggest charge is:

E⃗ (r⃗ )=Cr2r^

where C is a constant proportional come thecharge, r=∣∣r⃗ ∣∣,and r^=r⃗ /r is the unitvector in the radial direction.


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Transcribed picture text: part C What is the electrical flux Ф2 passing outward through surface 2? to express Ф2 in regards to r1, r2, C, and any constants or other well-known quantitie View easily accessible Hint(s) 2 Submit two hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are focused at a suggest charge and also are dealing with each various other so the their edges specify an annular ring (surface 3), as shown. The ar at position because of the point charge is component A what is the electrical flux ФЗ v the annular ring, surface 3? Express your answer in regards to C, r1, r2, and any constants. Where C is a consistent proportional to the charge, F, and also /r is the unit vector in the radial direction. View accessible Hint(s) igure 1 the 1 surface ar 2 surface 2 Submit surface 3 surface ar 3 part B E ficl surface ar 1 what is the electric flux Ф through surface 1 ? to express Ф1 in regards to C, r, r2, and also any needed constants. Surface ar 1 View obtainable Hint(s) Side view Front Vievw
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