q free on inner surface - q free on inner surface Interior points electric field must be zero - q bound + q bound Symmetry – fields must be uniform – field lines perpendicular to plates

conductordielectric Gauss’s Law

frequency dielectric constant

V = 0

B Fe H Fe B gap H gap B air H air i coil windings gap region iron core

width L thickness t area A q = - e electrons are the charge carriers in copper

dy F +q+q -q-q

Induced dipole moment – helium atom -e +2e Zero electric field – helium atom symmetric  zero dipole moment -e +2e -e A B effectively charge +2e at A and -2e at B dipole moment p = 2 e d

-q-q +q+q r 1  r – (d/2)cos  r 2  r + (d/2)cos  r  P ErEr EE (d/2)cos 

f+f -f-f     dA -b-b +b+b

+q+q -q-q

+f+f -b-b +b+b -  f O r S

- dd  r Pcos  S The area of the shaded ring between  and  + d  is equal to

a +Ze a d d << a