Using Gauss’ Law From flux to charge

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

Using Gauss’ Law From charge to the field

Uniformly charged planar surface

Uniformly charged spherical shell (outside)

Uniformly charged spherical shell (inside)

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

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.

Another example… -q +q

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

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

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

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.

No field in the hole.

Faraday cage

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

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.

Electric field just outside a conductor

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

Gauss’ Law for magnetic fields