Consider the rectangular conducting loop shown below where at a certain moment a time-varying
magnetic eld appears as shown. For dS given by ids, assume that you have calculated anegative
value for the induced emf in the loop. Draw an arrow indicating the

1. Given the vector field = 2! + 5 ! ! ! , determine the divergence of
at the point (2,3,6). answer: 26
2. Determine the magnetic flux through a cube, which has an area of 2 ! on each
side, if the cube is

Conservation of Power and the Poynting Vector
Note the following:
1 1 1
A A A A A A 2A A A A
2
t
t
2
t
t
t 2
Recalling the first two of Maxwells equations we can manipulate them as follows:
D
H Jc
t
D
E H E J c
t
D
E Jc E
t
E
E J

[n the gure below a rectangular planar surface 15 shown lying 1n the x- z Cartesian plane. It
is immersed 1n a time- -varying magnetic eld represented by B: ( 3xy + 3z)6 cos(10001tt) Wyz.
+x 5;! d5: %\
+Y
a. Calculate the value of the magnetic ux throug