Chapter 3 Fields of Stationary Electric Charges: II Solid angles Gauss' Law Conductors a Poisson's equation Laplace's equation Uniqueness Theorem - lmages
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 dl d sin e do integrating over the curve C yields d l sin e a=JC g radlan. (2 )Solid angle subtended by a surface(see Fig3. 3) a small element of area da subtends a small solid angle at P cos 8da r1. da integrating over a finite area S yields cos eda 2 steradian
If s is a closed surface containing p cos eda 4丌, steradian. If P is situated outside of S,(see Fig 3.4) cO s eda g2=/s-2=0
3.2 gauss’Law This law relates the flux of e thru a closed surface to the charge inside By using this law one can find e of simple charge dis- tributions easily Let a point charge q be at the point P inside the closed surface s. The flux of e thru a small element of area da is E. da Q r1. da Q d o 4丌∈0 4丌∈0 Integrating over yIelds JE da 4丌 4m∈0 4丌∈0
If several point charges Qi are inside th e fields is E=∑E2 The flux of e thru a small element of area da is E·da=∑E;da Integrating over S yields Q2;1 /sE.da=∑ ∑Q ∈ For a general distribution of charge inside s Q=/p(r')di so we have E da=o/p(r) The gauss law in integral form