Maxwell’s equations

constitutive relations D =  E  B =  H j =  E

Poynting’s theorem

em power that leaves = -  (stored em energy) /  t - lost em power E x H

Spherical radiation E x H ds = EH 4  2  E 2 4  2  constant E  1/  

Cylindrical radiation E x H ds = EH 2  r L  E 2 2  r L  constant E  1/(r) 1/2 r L

r d V = V o cos  t = 2  rH 

Boundary conditions E1E1 E2E2 B1B1 B2B2 Pillbox  SLoop  L components

Integral form of Maxwell’s equations

Normal component of B B n1  s + B n2  s = 0 B n1 B n2 Normal components of B are continuous No magnetic monopoles!!

Normal component of D D n1  s + D n2  s =  s  s D n1 D n2 Normal components of D differ by surface charge density Electric charge

Tangential component of H H t1  L + H t2  L = j s  L H t1 H t2 Tangential components of H differ by surface current density surface current

Tangential component of E E t1  L + E t2  L = 0 E t1 E t2 Tangential components of E are continuous

example  1 = 1  2 = 4

example  1 = 1  2 = 4 y

example  1 = 1  2 = 4 y

Tangential components of the electric field intensity are continuous Normal components of the displacement flux density differ by a surface charge density Normal components of the magnetic flux density are continuous Tangential components of the magnetic field intensity differ by a surface current density

Tangential component of E metal    E t1  L + E t2  L = 0 E t1 E t2 Tangential component of E is zero. but E t2 = 0

images Charge +Q Equipotential contours Electric field E Image charge -Q Equipotential contours Electric field E

images

Charge +Q Image charge -Q 2d Image charge –Q Image charge +Q

Antenna on top of the ground Underneath an antenna is an array of conductors This creates a ground plane This effectively makes the antenna twice as tall

an egg – after an egg – before tooth pick CD microwave oven experiments -- dangerous aluminum foil