E&M 2

Maxwell’s equations are:

(SI units)
or, in macroscopic form:
In lih materials with

we have:

The method of images

Consider a charge q at  z = d on the z - axis.
Assume the z = 0 plane is a grounded conducting plane.  Then placing an image charge 
q’ = -q at  d’ = -d on the z-axis makes the z = 0 plane an equipotential with Φ = 0. 
The electrostatic field and potential above the plane are the same as the field and potential due to the charge and its image charge.

AC circuits

Assume V(t), I(t), emf(t) are all proportional to exp(iωt).   Assume idealized circuit elements.  Define the impedance Z = V/I.  Then

    

Kirchhoff’s rules for filamentary circuits:   For each loop ∑nVn = 0  for each node  ∑nIn =0.
Any two-terminal network of passive elements is equivalent to an effective impedance Zeff
Thévenin equivalent circuits: Any two terminal network can be replaced by a generator emfeff in series with an impedance Zeff.

Example Problems:  (Solutions)

Problem 1:

Problem 2:

Problem 3:

Problem 4:

Problem 5:

Problem 6:

Problem 7:

Problem 8:

Problem 9:

Problem 10: