Chapter 22

Question 1

What is a Gaussian surface

Answer 1

• An imaginary closed surface that encloses a certain amount of charge
• Used to relate E on this imaginary surface to Qenc via electric flux

Question 2

What is electric flux

Answer 2

• Flux is a measure of how much/how strongly the field (E) points though (outward from Qenc) the surface
• Flux ⊥ E and flux ⊥ A (as vectors)

Question 3

When max, min flux

Answer 3

max: E ⊥ A , Φ = EA or max negative Φ = -EA
min: E points alond the surface and not at all through it , i.e. E // A , Φ = 0

Question 4

Two main complications for Φ in the general case

Answer 4

1. E can be non-uniform, i.e. E(r) varies from point to point on surface (our GS)
2. the surface is curved, i.e. ^n varies from point to point

Question 5

Gauss’ Law

Answer 5

The total electric flux though a closed surface (the GS) is equal to the new electric charge enclosed by the GS, divided by ε0

Question 6

2 important remarks on using Gauss’ Law

Answer 6

1. Φ depends only on Qenc, shape/size of GS is irrelevant
2. Charges outside the closed surface cannot contribute to the total Φ through the surface. if Qenc = 0, Φ = 0 even if E != 0 (what goes in would go out and they would “cancel”)

Question 7

E field outside any SSCD is the same as..

Answer 7

is exactly the same as that if a point charge with charge Qtotal located at the center of the SSCD

Question 8

E field inside an empty hollow SSCD (cavity) non conducting case

Answer 8

E =0 everywhere inside the cavity, Qenc = 0, a charge would thus experience no forc, due to symmetry everything cancels

Question 9

E in conductor:

inside a conductor in electrostatic equilibrium

Answer 9

the elctric field E is zero everywhere

• this is true even if the filed outside != zero
• if this were not true then there would be a net E , thus a non zero Fnet thus we would not be in electrostatic equil.

Question 10

E in conductor:

Conductor with net charge Qc

Answer 10

Qc must lie on the outersurface of the conductor
- Inside conductor E =0, thus Φ through any GS = 0, thus any excess charge (Qc is all excess) must lie on the outer surface

Question 11

E in a conductor:

charge on surface of empty cavity

Answer 11

0 , There will be no net charge on the surface of an hollow cavity inside the conductor
- Since E = 0 everywhere inside Φ through any GS =0, then by Gauss’ Law Qenc = 0

Question 12

E in conductor:

If Qenc!=0

Answer 12

If there is net charge Q in cavity inside conductor, the charge will be screened by an opposite charge on rhe cavity surface
- Since E=0 inside, Φ though an GS =0, thus there must be a surface charge to cancel out Q in the cavity (by Gauss’ Law Qenc = 0?)