Review Electostatic D. Ray Kwok SJSU
Paty Balloons
Coulomb s Law F e q q k 1 Coulomb foce o electical foce. (vecto) Be caeful on detemining the sign & diection. k 9 10 9 (N m / C ) k 1 4πε o k is the Coulomb s constant, ε o is called pemittivity of vacuum, fo now it s just a constant. ε o 1 4πk 9 10 36π 8.84 10 1 C N m
Electic Field Lines (F qe) Think of the diection of coulomb foce on a + test chage geneate fom a + chage teminate into a - chage
Two opposite chages
Othe combinations
Conducto & E-field: Popety 1 The electic field is zeo eveywhee inside the conducting mateial Conside if this wee not tue If thee wee an electic field inside the conducto, the fee chage thee would move and thee would be a flow of chage If thee wee a movement of chage, the conducto would not be in equilibium. (Electostatic!!)
Popety Any excess chage on an isolated conducto esides entiely on its suface A diect esult of the 1/ epulsion between like chages in Coulomb s Law If some excess of chage could be placed inside the conducto, the epulsive foces would push them as fa apat as possible, causing them to migate to the suface So E 0 inside.
Popety 3 The electic field just outside a chaged conducto is pependicula to the conducto s suface Conside what would happen it this was not tue The component along the suface would cause the chage to move It would not be in equilibium
Popety 4 On an iegulaly shaped conducto, the chage accumulates at locations whee the adius of cuvatue of the suface is smallest (that is, at shap points)
e.g. Metal shielding Place a point chage inside a conducting shell. E field lines ae pependicula to the suface. E 0 inside conducto. Chages ae induced on the suface.
E field of a chaged conducto iegula shape E field lines ae pependicula to the suface. E 0 inside conducto. Chages ae cumulated on the suface. E field is moe intense at small adius (highe concentation of chages)
Chage distibution A non-conducting thin wie of m long, caying a chage density of +10µC/m. What is the electic field at 10 cm fom the cente of the wie? Notation used in most textbook ρ volume chage density σ suface (aea) chage density λ linea chage density dy y x θ de dq de k de x E ( dy) 1( x + y ) ( λdy) + de cosθ k x 1 kλx k x 3 / y ( λdy) x kλx( dy) + y (x is a constant 10 cm) ( x + y ) 3 / 1 1 dy 3 ( xsec θ) dy 1 3 x xsec θdθ 1 3 x 1 y x + y 1 1 1 cos θdθ sin θ x x 1 0.1 ( ) 199 0.1 + 1 y x + y 1 dy 9 5 6 E kλx ( 9 10 )(10 )(0.1)(199) 1.8 N/C, to the ight 1 3 10
Gauss In cgs, gauss is the unit fo magnetic field. Many contibutions in math and geophysics. Most known fo his electostatic wok. Known as the Gauss s Law. Cal Fiedich Gauss Geman mathematician & scientist 1777-1855
Electic Flux Field lines penetating an aea A pependicula to the field The poduct of EA is the flux, Φ In geneal: Φ E E A cosθ Φ E E da
Gauss Law Gauss Law states that the electic flux though any closed suface is equal to the net chage Q inside the suface divided by ε o E inside ε o is the pemittivity of fee space and equals 8.85 x 10-1 C /Nm The aea in Φ is an imaginay suface, a Gaussian suface, it does not have to coincide with the suface of a physical object Φ E da Q ε o Q inside ε o
Total flux does not depends on the shape chosen
Gaussian Suface Have the same symmety as the chage distibution, such that E field is unifom on the suface E field is pependicula to the suface ΦE E da EA EA Q inside ε o
e.g. Point Chage Gaussian suface is a sphee EA ( π ) E 4 E Q ε 1 4πε inside o o q ε o q which is the E field fo a point chage
E field of a line o plane of chage infinite plane of chage infinite line chage
E field of a unifomly chaged sphee
Divegence Theoem o Gauss s Theoem V EdV S E da fo any vecto E. Gauss s Law V Qinside E da ε o ρdv EdV ε V o ρ E Gauss s Law in diffeential fom ε o
Stoke s Theoem S E da L E d l fo any vecto E. In electostatic, we defined electic potential (voltage): and L E d l 0 Consevative field, Kichhoff s ule. E 0 V E d l L