Electric flux, Gauss’s law Carl Friedrich Gauss Physics 122 11/14/2018 Lecture IV

Concepts Primary concepts: Electric flux 11/14/2018 Lecture IV

Laws Gauss’s law 11/14/2018 Lecture IV

Definition of electric flux Flux means flow Nothing is actually flowing Other than that thinking of flow really helps to understand the flux 11/14/2018 Lecture IV

Electric flux If electric field is rain – electric flux is the amount of water in a bucket accumulated per unit of time: Only component of the field perpendicular to the area A contributes to the flux 11/14/2018 Lecture IV

Electric flux Alternatively we can define a vector A, which equals to the area A and is directed perpendicularly to the area Flux is proportional to the number of field lines going through the surface 11/14/2018 Lecture IV

Compare fluxes Which flux is larger? 2 1 Which flux is larger? 1). F1>F2 2). F1<F2 3). F1=F2 11/14/2018 Lecture IV

Compare fluxes Which flux is larger? 2 1 Which flux is larger? 1). F1>F2 2). F1<F2 3). F1=F2 11/14/2018 Lecture IV

Compare fluxes Which flux is larger? 1 2 Which flux is larger? 1). F1>F2 2). F1<F2 3). F1=F2 11/14/2018 Lecture IV

Compare fluxes Which flux is larger? 1 2 Which flux is larger? 1). F1>F2 2). F1<F2 3). F1=F2 11/14/2018 Lecture IV

Compare fluxes Which flux is larger? 1 2 Which flux is larger? 1). F1>F2 2). F1<F2 3). F1=F2 11/14/2018 Lecture IV

Compare fluxes Which flux is larger? 2 1 Which flux is larger? 1). F1>F2 2). F1<F2 3). F1=F2 11/14/2018 Lecture IV

Non-uniform field, irregular surface Closed surface Influx <0 Outflux>0 Don’t worry, we’ll only deal with simple surfaces Complex surfaces can be handled using numeric integration by a computer. 11/14/2018 Lecture IV

Why do we need flux? Gauss’s law: 11/14/2018 Lecture IV

Gauss Coulomb Calculate E of point like (+) charge Q Consider sphere radius r centered at the charge Spherical symmetry: E is the same everywhere on the sphere, perpendicular to the sphere 11/14/2018 Lecture IV

Sinks and sources What goes in – goes out unless there is a source (positive charge) or a sink (negative charge) + - 11/14/2018 Lecture IV

What’s the flux? F1=? F2=? 11/14/2018 Lecture IV

Respect the symmetry Find electric field for the following configurations: Uniformly charged sphere. Charge Q, radius R. Long uniform line of charge. Charge per unit length l. Infinite plane of charge. Charge per unit of area s 11/14/2018 Lecture IV

Field near conductor Infinite plane of charge. Charge per unit of area s Field inside conductor is zero, outside perpendicular to the surface. 11/14/2018 Lecture IV

Respect the symmetry Find electric field for the following configurations: Uniformly charged sphere. Charge Q, radius R. Long uniform line of charge. Charge per unit length l. Infinite plane of charge. Charge per unit of area s 11/14/2018 Lecture IV

Two parallel plates + - Infinite plates One positive, one negative, Same charge density s + - 11/14/2018 Lecture IV