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

XXXXXXXXXXXX Circulation loop: square of length L Cross-section through electromagnet Current i out of page Current i into page

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

+ -

dy F +q+q -q-q

x L-x V rr C = C A + C B

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

Induced dipole moment – sulfur atom -8e +16e Zero electric field – helium atom symmetric  zero dipole moment -8e +16e -8e A B effectively charge +16e at A and -16e at B dipole moment p = 16 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

F F F d +Q+Q - Q 

0 π/2 π 0 + p E - p E  U

T PoPo

p E / k Tp E / k T slope = 1/3

non-conducting liquid air conducting sphere q a Gaussian surface S r Symmetry  field lines must be radial

non-conducting liquid air conducting sphere q Symmetry  E airt = E liquidt  E air = E liquid = E E airt E liquidt

field lines of E field lines of D

+ - induced dipoles due to shift in electron cloud rotation orientation of polar molecules - + shift in atoms due to ionic nature of bond

NS H Fe H air Circulation loop: square side L 5 6

B-field lines – form continuous loops Gauss’s Law for magnetism Cylindrical Gaussian surface

Bound surface currents (right hand screw rule)  N pole

un-magnetized piece of iron N Bar magnet bought near un-magnetized piece of iron N N  Bar magnet will attract the iron that was initially un-magnetized north pole attracts south pole

Fe ramp Cu ramp plastic ramp N N N

Circulation loop for circulation integration used in applying Ampere’s Law N N H iron H air

d ifif ifif