Electric flux Gausss law Carl Friedrich Gauss Physics

Electric flux, Gauss’s law Carl Friedrich Gauss Physics 114 9/9/2020 Lecture III 1

Concepts • Primary concepts: – Electric flux 9/9/2020 Lecture III 2

Laws • Gauss’s law 9/9/2020 Lecture III 3

Definition of electric flux • Flux means flow • Nothing is actually flowing • Other than that thinking of flow really helps to understand the flux 9/9/2020 Lecture III 4

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 9/9/2020 Lecture III 5

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 9/9/2020 Lecture III 6

Compare fluxes 2 1 Which flux is larger? 1). F 1>F 2 2). F 1<F 2 9/9/2020 Lecture III 3). F 1=F 2 7

Compare fluxes 2 1 Which flux is larger? 1). F 1>F 2 2). F 1<F 2 9/9/2020 Lecture III 3). F 1=F 2 8

Compare fluxes 1 2 Which flux is larger? 1). F 1>F 2 2). F 1<F 2 9/9/2020 Lecture III 3). F 1=F 2 9

Compare fluxes 1 2 Which flux is larger? 1). F 1>F 2 2). F 1<F 2 9/9/2020 Lecture III 3). F 1=F 2 10

Compare fluxes 1 2 Which flux is larger? 1). F 1>F 2 2). F 1<F 2 9/9/2020 Lecture III 3). F 1=F 2 11

Compare fluxes 2 1 Which flux is larger? 1). F 1>F 2 2). F 1<F 2 9/9/2020 Lecture III 3). F 1=F 2 12

Non-uniform field, irregular surface • Closed surface • Influx <0 • Outflux>0 9/9/2020 Don’t worry, we’ll only deal with simple surfaces Complex surfaces can be handled using numeric integration by a computer. Lecture III 13

Why do we need flux? • Gauss’s law: 9/9/2020 Lecture III 14

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 9/9/2020 Lecture III 15

Sinks and sources • What goes in – goes out • unless • there is a source (positive charge) + • or a sink (negative charge) 9/9/2020 Lecture III 16

What’s the flux? • F 1=? 9/9/2020 F 2=? Lecture III 17

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 9/9/2020 Lecture III 18

Field near conductor • Infinite plane of charge. Charge per unit of area s • Field inside conductor is zero, outside perpendicular to the surface. 9/9/2020 Lecture III 19

Two parallel plates • Infinite plates • One positive, one negative, • Same charge density s + 9/9/2020 Lecture III 20