Electricity Electric Flux and Gausss Law Electric Flux

Electricity Electric Flux and Gauss’s Law Electric Flux Gauss’s Law Electric Field of Spheres Other Gaussian Surfaces Point Charges and Spheres 1

Electricity Electric Flux and Gauss’s Law Flux is defined as the amount of an electric field passing perpendicularly through a surface. For an electric field passing perpendicular to a plane, it is… E A 2

Electricity Electric Flux and Gauss’s Law What if the electric field is not perpendicular? A E θ A 3

Electricity Electric Flux and Gauss’s Law What if the surface is a closed surface? E q 4

Electricity Electric Flux and Gauss’s Law In general, Gauss’ Law states that for any imaginary closed surface Gauss’ law is always true but not always useful. Qinside is the charge inside the imaginary surface. F is the total flux through this surface. We use Gauss’ law to calculate E. Gauss’ law is easy to use if the electric field vector is perpendicular to the chosen surface. ) 5

Electricity Electric Flux and Gauss’s Law Rules for Conductors All excess charge within a conductor moves to its surface. The electric field inside the material that makes up a conductor is zero. Electric fields just outside the surface of a conductor are perpendicular to its surface. Gauss’s Law is usually the best way to find the electric field of a conductor. 6

Electricity Electric Flux and Gauss’s Law Outside any Sphere A sphere with total charge Q from Gauss’ Law Q r An imaginary Gaussian surface The electric field 7 The electric flux E

Electricity Electric Flux and Gauss’s Law Outside any Spherical Shell Gauss’ Law Q r E The electric field 8 The electric flux

Electricity Electric Flux and Gauss’s Law Inside any Spherical Shell Q R r E The electric field 9 The electric flux Gauss’ Law

Electricity Electric Flux and Gauss’s Law For a cylinder or a plane, the principal is the same but the surface used changes Note that the end faces must be included unless the cylinder is infinitely long. En En 10

Electricity Electric Flux and Gauss’s Law Outside a Conductor with a Point Charge Inside The electric flux Q Gauss’ Law q r E The electric field 11

Electricity Electric Flux and Gauss’s Law Inside a Conductor with a Point Charge Inside The electric flux Q q R r E The electric field 12 Gauss’ Law

Electricity Electric Flux and Gauss’s Law Outside a Conductor with a Point Charge Outside The electric flux Q Gauss’ Law r q E The electric field 13

Electricity Electric Flux and Gauss’s Law Inside a Conductor with a Point Charge Outside (it works as a shield and lets no electric field inside its walls) The electric flux Q R r q E The electric field 14 Gauss’ Law