1. Using Gauss’ Law
From flux to charge

2. How much charge is inside the cylinder (圆柱)?
E = 550 N/C
r = 5 cm
L = 15 cm

3. Using Gauss’ Law
From charge to the field

4. Uniformly charged planar surface

5. Uniformly charged spherical shell (outside)

6. Uniformly charged spherical shell (inside)

7. Uniformly charged cube
Problem: The field is not uniform over each surface. So we can’t take E outside the flux integral.

8. Gauss’ Law is only useful when the field has a certain symmetry.
Be careful: the law is always true, even when there is no symmetry.

9. Another example… -q +q

10. A charged conductor – where does the charge go?
Gaussian surface
Net charge is zero inside a conductor.

11. Excess charge in a conductor is always on the surface.
Gaussian surface
Net charge is zero inside a conductor.

12. What if there is a hole?
Net charge is zero inside the Gaussian surface.

13. Could there be a field in the hole?
The change in potential ΔV from A to B must be zero.
So the field inside the hole must be zero.

14. No field in the hole.

15. Faraday cage

16. What if there is a charge in the hole?
Net charge is still zero inside the Gaussian surface.

17. What if there is a charge in the hole?
The net charge on the conductor is still Q, but some negative charge has moved to the surface of the hole.

18. Electric field just outside a conductor

19. Gauss’ Law for magnetic fields
There are no magnetic “charges”.

20. Gauss’ Law for magnetic fields