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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 rr 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 EE (d/2)cos
f+f -f-f dA -b-b +b+b
+f+f -b-b +b+b - f O r S
- dd 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
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
q free on inner surface - q free on inner surface Interior points electric field must be zero - q bound + q bound Symmetry –
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