Presentation on theme: "Gauss law More fundamental statement about electric fields than Coulomb’s law.More fundamental statement about electric fields than Coulomb’s law. Easily."— Presentation transcript:
Gauss law More fundamental statement about electric fields than Coulomb’s law.More fundamental statement about electric fields than Coulomb’s law. Easily calculate electric field for highly symmetric continuous charge distributions.Easily calculate electric field for highly symmetric continuous charge distributions. Understand the properties of conductors in electrostatic equilibrium.Understand the properties of conductors in electrostatic equilibrium.
Overview Charge symmetry determines electric field symmetry. Calculate electric flux (number of electric field lines) through a surface. Gaussian surfaces: Just a closed surface around a charge. Gauss law: The electric flux through a Gaussian surface is related to the charge inside the surface.
Symmetries The electric field must match the symmetry of the charge distribution!
The symmetry argument Electric field must match the symmetry of the charge distribution!
Concept Quiz What best describes the electric field symmetry outside the charged conducting sphere? A)Radially inward B)Radially outward C)Zero field D)Concentric - - - - - - - - - -
Concept of flux Important analogy: Air flowing through a loop. The amount of air through the loop depends a) on the size of the loop, b) on the angle of the loop with respect to the air flow. Rate of air flow through the loop:
Area as a vector quantity Vector is uniquely defined by a) magnitude b) direction. So we define the magnitude as the size of the area (π r 2,a x b, etc). And we define a direction by a unit vector perpendicular to the area
Electric flux The electric flux due to an electric field E through area A = the number of electric field lines through A
Electric flux If the electric field is not uniform, we have to sum up many small fluxes all over the area: The meaning of the surface integral that it sums over many small fluxes. It is a mathematical tool.
1)Electric field everywhere tangent to surface: 2) Electric field everywhere perpendicular to surface and same magnitude E at every point:
Flux through closed surface Definition: The area vector points from inside to outside
Concept Quiz What is the electric flux through the cylinder with height h and radius r? A) Zero B) E 2 r h C) E (2 r 2 +2r h ) D) Eh r 2 h h r