HYPERPHYSICS  NOTE: THIS HYPER PHYSICS LINK , INDUCTION, 
QUIZ 9   ~   CH. 29
EXERCISES/PROBLEMS
Case i:  Area = constant; B changes with t.
Case ii: Area is not constant; B is constant in time t
Case iii: Compute the electric field w or w/o a wire.
Case i: 6, 8, 52
Case ii: rotator generator 54, and example 29.4; slide wire generator: 24, 31, 27
More Case i: 15, 16
More Case ii: motional emf ~ 23, 33  and 31, 27
Case iii: 36, 71
DISPLACEMENT CURRENT: 42.
 Many of these problems were reviewed in class, directly or indirectly,  with reinforcement from the Faraday's Lab. Here is a couple of hints on some  problems with different  perspectives on the subject of "induction" : 
71. We reviewed this in class, but it does not hurt to repeat. 
For background to #71, reviewed in class, see equation 29.11 and figure 29.17 (b); What is important is the external MAGNETIC field  points IN and is increasing in magnitude.  Thus the electric field is "counterclockwise" in orientation in on the  loop shown.

Now see figure P29.71.  We see the same situation, external B points IN with increasing magnitude. So the induced electric field will also be "counterclockwise" in orientation at points a and b. The result is similar to having a wire loop in which the induced magnetic field would be OUT to oppose the change in the external magnetic field and  in which the induced current would flow counterclockwise.  In this case, this  means at point a, the ELECTRIC field points left, and at point b, the electric field points up.  

To get equation 29.11, use: E*(2*pi*r ) = Area*| dB/dt | =  pi*r2*| dB/dt | .
Thus,  the electric field magnitude E = (r/2)*|dB/dt| . This is the symbolic answer, with the direction of the electric field vector counter-clockwise in orientation . 
Note at point c, E = 0 according to the formula.
 42. Look over section 29.7.  
(a) jD   = iC/(pi*R2), where R = 0.0400 m. 

(b) (epsilon)*pi*R2*dE/dt = iD = iC = 0.280 (A).  Find dE/dt.  Note from conservation  of charge, conduction current iC = displacement current iD

(c) and (d):  Use formula 29.17; R is given. Substitute r into the formula and  try to understand the derivation of formula. Note from conservation  of charge, conduction current iC = displacement current = iD