Student Questions from Cook Chapter 160:

1. Why can we not derive an extension of the static field equations to make equations for the time-dependent fields?

Some totally new phenomena are observed when we let the fields depend on time. New phenomena can rarely be predicted, it must be observed and then incorporated into the body of theory.

2. I don't really have any questions for this chapter, except the example in 160.3 of the wire separated by plates. Can this situation actually occur, current just jumping over a gap like that?

Current is NOT jumping over the gap in Fig. 160.1. Current is flowing toward the left hand plate, charging it positively, and away from the right hand plate, charging it negatively. This is the classic example that is used to motivate the addition of a new term to the right hand side of Ampere's Circuital Law. The left side of Ampere's Law is the integral around a closed path of B dot dl. The right side is mu-nought time the current passing through a surface that is bounded by the closed path... any surface! In the example illustrated in Fig. 160.1, it appears that we get different answers on the right hand side of Ampere's Law depending on whether we choose the flat surface bounded by the closed path or the "chef's hat" surface that is also bounded by the closed path. No current passes through the chef's hat. So, in order to be mathematically consistent, we need to add a new term to the right hand side of Ampere's law... a term that is proportional to the rate of change of ELECTRIC flux through a surface bounded by the closes path. The author shows on page 16003 that the rate of change of electric flux (times mu_o*eps_o) through the chef's hat is the same as mu_o*I_enclosed through the flat surface. Thus the answer is independent of the surface chosen as it must be because the left hand side of Ampere's law is independent of the surface chosen.

3. Please explain why the example in 160.3 is acceptable. Why are you allowed to spilt the wire?

We are allowed to do anything we can imagine constructing. There is no reason to believe we could now construct the example shown in Fig. 160.1. See answer to question #2.

4. is chapter 160 really only four pages long with no questions, or is my book missing pages?

You are not missing anything.

5. What does that integral with the circle through it mean again? I know it is something on a closed surface. Does it just mean the total of whatever the right hand side of the equation specifies (i.e. does what it signifies vary from equation to equation?).

It either signifies a path integral over a CLOSED PATH, in which case the qualifier "closed path" is indicated below it, OR is signifies a surface integral over a CLOSED SURFACE, in which case the qualifier "closed surface" is indicated below it. In some texts you may see the closed surface integral indicated by a double integral with a circle over it to remind you that it is a two dimensional integral... a surface integral.

6. also, i really do not understand figure 160.1. Could you please elaborate on it?

See answer to question #2 above.

7. I'm still unclear about changing fields (B or E) producing the other kind (E or B). How does a B-field produce an E-field, or vice versa.

How does mass exert a gravitational force? How does charge exert an electric force? These are questions in the same vein as your question. One can attempt to answer them with a theory that is "one level deeper" than the theories we are describing in this course... general relativity and quantum electrodynamics respectively. At this point I do not think that is the anwer you are searching for. Rather, you are struggling to assimilate a phenomena with which you are not very familiar and have no direct experience with. Does the following answer leave you unsatisfied?... "We observe that a changing magnetic field can produce an electric field... AND we observe that a changing electric field can produce a magnetic field." 

8. In the generalized circuital law the book talks about two surfaces. What are they?

Actually it applies to an infinity of possible surfaces. The left side of the equation is the close path integral of B dot dl. The right side has two pieces that in general must both be included to satisfy the law. The first piece is the electric current (times mu_o)  through a surface (ANY SURFACE) bounded by the close path. The second piece is the rate of change of the electric flux (times mu_o*eps_o) through that surface. Any surface that has as its edge the closed path used on the left hand side to perform thepath integral should yield the same answer. On page 16003, the author shows that one gets the same answer for two specially chosen surfaces... one that is the flat surface spanning the closed integration path through which the current is non-zero, but the electric flux change is zero. The second surface is a chef's hat surface through which there is no electric current, but there is a changing electric flux. The changing electric flux comes about because the current passing through the first surface is piling up charge on the left hand plate in Fig. 160.1, charging is positively and is taking away (+) charge from the right hand plate, leaving it charged negatively.

9. I'm having a hard time understanding what the problem is in 160.3. Is it that the electrons are not carried by a wire between the two plates? Does current have to travel through a wire?

Yes, current usually has to travel through a wire. No current is passing across the gap between the plates in Fig. 160.1. See answers to questions #2 and #8 above.

10. I don't understand the surface described on page 16002 that makes Ampere's law invalid for changing fields.

See answers to questions #2 and #8 above.

11. I found this chapter a very nice and helpful summary, but I am still somewhat uncertain as to the meaning of a time dependent field. I think an example would help me out a lot.

Almost all real fields are time-dependent. The temperature of the air in this room is a scalar field and is time-dependent. If you were to measure the temperature at any point (or every point) in space, it would vary with time. That is a time-dependent scalar field. The flow velocity of the air in the room is a time-dependent vector field. As the HVAC system kicks in and blows air into the room while withdrawing it elsewhere, the pattern of flow through the room changes. That is a time-dependent field. Up to this point we have considered the somewhat rare case of static electric and magnetic fields because they are easier to deal with at the beginning.

12. On Faraday's Law: The negative sign accounts for a positve change in the flux. What does the negative charge account for? Because for the positive we infer an opposite reason to the negative sign, then do we infer a positive fro the negative? I do not get it...

Let the minus sign simply be a reminder to you to use Lenz's Law to determine the direction of an induced emf. Imagine placed a loop of wire in the location where the induced emf is desired to be known. Determine the direction of the magnetic flux through the loop AND whether it is increasing or decreasing in magnitude. The direction of the induced emf will be in the sirection such that the current drivein in the loop would produce a magnetic field through the loop that opposes the change that induced it.

13. There a statement Induced flux is opposite to inducing flux, it is said to be wrong but can be proven right, how? The book does not to in depth on this subject. Is it then that induced is equal and opposite to inducing flux?

The flux produced by an induced current is in the direction to oppose the change in flux that induced the current. This is a statement of Lenzs Law. I did an example in class. If you are still confused, please see me.

14. How come Fraday''s Law is a derivative with respect to time if we cannot deduce the position of a particle goning through a wire it is relative as far as I know!What makes fields time-dependant? I believe they are not but the derivative.

I am not sure I uderstand the question. A field is time-dependent if its magnitude or direction changes with the passage of time. the description of that field... perhaps even whether it is a magnetic field or an electric field might depend on your reference frame... on your state of motion relative to the source of the fields, but within a single reference frame, one can observe fields to change in time. One can apply Maxwell's equations in any (inertial) reference frame and obtain correct answers... that agree with experiment, even though another observer might obtain different numerical values for most measured quantities.

15. Do all four of the maxwell equations involve the lorentz force equation?

The Lorentz force completes classical electromagnetic theory by determining the motion of charged particles under the influence of the electric and magnetic fields that satisfy Maxwell's equations. The positions and velocities of the charged particles then affects the electric and magnetic fields. In general it is a highly "nonlinear" problem.
 
16. Why is the magnetic flux law shown to be equal to 0 in the equation 160.13?

This is the same as we saw in chapter 150 (Eq. 150.32). It is a mathematical statement of the qualitative statements that 1) magnetic field lines never begin or end, 2) there are no magnetic charges, 3) every magneti has both a N and a S pole, 4) the net magnetic flux through a closed surface is zero.