1. First Term Stuff
If you want to make up labs or quizzes from Term 1, see me before the end of this week to make a plan
If you have already seen me, you are good

2. Electric Flux
how many lines?

3. Electric Flux
Through a closed surface

4. Electric Flux FE
Conceptually, the number of electric field lines passing through a surface E
FE = EA
A = area of the surface

5. Electric Flux FE
Previous formula only works when field is normal to the surface E
FE = 0

6. Electric Flux FE E q Area in profile is A cos q
q = angle of E field from surface normal
FE = EA cos q = E·A
A = “Area vector” normal to surface

7. Electric Flux
Integrate over entire surface
FE = ∫E·dA

8. Surface Integral
Around an entire surface that encloses a region of space
Symbol ∫
Area vector points outward

9. Gauss’s Law
Flux through an enclosing surface is proportional to charge enclosed
FE = q/e0
e0 = “vacuum permittivity” = 8.85×10–12 C2/(Nm2)

10. Gauss’s law Use flux to find field around a point charge
The answer should be Coulomb’s law

11. Field of a Point Charge What is area A of spherical shell?
AP Physics L04_flux
Field of a Point Charge
What is area A of spherical shell?
FE = Qin/e0 = EA
Find E

12. Field around a Point Charge
Shell Area = 4pr2
FE = q/e0 = EA +q q
e0A q
e04pr2 R
E = = q
4pe0 r2 = kq r2 =
if k = 1
4pe0

13. Gauss’s Law Example Infinite line of uniform charge density (Q/L) = l
Cylindrical surface with charge on axis
Area of surface = 2prL + ends
Qin = Ll
FE = Qin/e0 = Ll/e0
FE = E(2prL)
Ll/e0 = E(2prL)
2pe0 1 l r
E = Q

14. Gauss’s Law Example Infinite plate of uniform charge density (Q/A) = s
Area of surface = 2A + edges
Qin = As
FE = Qin/e0 = As/e0
FE = E(2A)
As/e0 = E(2A)
E = ½ s/e0 Q

15. Gauss’s law examples
Field within a spherical shell of uniform charge density
Field within a sphere of uniform charge density
Charge distribution in a conductor
Field around charge at center of a neutral, hollow conducting sphere