Chapter 3 Fields of Stationary Electric Charges: II Solid angles a Gauss Law Conductors a Poissons equation Laplace's equation a Uniqueness theorem -Images
Chapter 3 Fields of Stationary Electric Charges : II ◼ Solid Angles ◼ Gauss’ Law ◼ Conductors ◼ Poisson’s Equation ◼ Laplace’s Equation ◼ Uniqueness Theorem ◼ Images
3. 1 Solid angles (1) Angle subtended by a curve (see Fig 3. 1 a small segment of curve dl subtends a small angle at p sin t integrating over the curve C yields d l sin e 2 raglan (2 ) Solid angle subtended by y a surtace(see Fig3.3 a small element of area da subtends a small solid angle at p do cos Ada r1. da integrating over a finite area s yields cos oda .2, Steradian
If s is a closed surface containing P cos eda 2 4丌, steradian If P is situated outside of S, (see Fig 3.4) cos ede 92=/s
3.2 Gauss’LaW This law relates the flux of e thru a closed surface to e charge Inside By using this law one can find e of simple charge dis tributions easily Let a point charge be at the point p inside the closed surface s. the flux of e thru a small element of area da is Q ri da Q a 4丌∈0 4∈0 Integrating over S yields /E·da=4丌e0 /ds 4丌 4丌∈0
If several point charges Q i are inside the fields is E=∑E The flux of e thru a small element of area da is E·da=∑E;:da Integrating over S yields Is E. da Q ∈0 ∈0 For a general distribution of charge inside s Q=/ p(r) so we have Is E da The gauss' law in integral form