| Date |
Question |
Answer |
| May 13 | Do we need to reference every equation we do not explicitly derive (such as solutions to Laplace's equation or the relation between spherical harmonics and Legendre polynomials * e^im(phi)) or just equations and ideas not regularly used in the techniques we use? | No, you don't need to reference every equation. Solutions of Laplace's equation should be considered "obvious" at this point. Ditto Maxwell's equations and boundary conditions. What you do need to reference are such things as particular fields (such as the B you used in P 5.12). |
| May 13 | I was just curious what a boss is. | Please refer to P 2.10 which was discussed in class. I also recommend a dictionary. |
| May 13 | Is hemisphere a hollow shell, or does it have a bottom that charge can sit on as well? | There is no bottom. |
| May 12 | Final problem 2.(d). It says " What is the electric field?" Does the condition r>> a apply? | Yes |
| April 1 | Prob 4. Is the 3.5 GHz the lowest cutoff frequency, or it could be any one ? Is the 3.6 GHz a cutoff frequency? Do all the field components refer to Et and Bt in each mode? |
It is "the" cutoff frequency, not "a" cutoff frequency. (We discussed this in class.) No, the cutoff frequency is 3.5 GHz. All the field components means all components of both E and B in all modes that exist. |
| March 31 | In problem 4, are we assuming the copper tube acts like a perfect conductor? (no energy loss) Also can we assume in air that epsilon = epsilon_naught and mu = mu_naught, or do we need to make the small corrections for these in air as opposed to vacuum? |
Yes Yes,no |
| March 29 | Exam problem 3. I was wondering if you wanted the lengths of the sides of the triangle to be left as arbitrary constants or if you wanted a particular length value assigned to them? | The result should not depend on those lengths. |
| March 22 | I am trying to solve part (b) of the problem 3.12. Jackson in the section 3.13 has a similar discussion which refers to the result of part (c) problem 3.16. Do I have to prove that or I can simply use that result? | I hope you noticed that Problem 3.16 c is due April 5! So you will have to prove it eventually. For now, you may just use the result. However, do be careful. Section 3.13 discusses a different problem with Mixed Boundary conditions (see also my notes http://www.physics.sfsu.edu/~lea/courses/grad/mixedbc.PDF). Problem 3.12 is not a case of mixed boundary conditions- it is a straight Dirichlet problem. |
| March 7 | For 2.26 part b (relevant for 2.27 as well) Jackson says "Keeping only the lowest nonvanishing terms..." Is it sufficient to keep only the lowest order (n=1) terms, or do we need to take more than one n? (The pluralization of term(s) is throwing me off, I know there is more than one term per value of n, but I wanted to make sure we only need to take the one lowest order of n.) | Yes, one value of n. |
| Feb 29 | I'm trying to sum the series and I got stuck very badly, if you can help me I would be very thankful. I believe that C=Q/V, where Q is the total charge on the spheres and V is the potential at he surface. I'm trying to sum the potential due to each image charge at the point exactly between the two centers. Is this the correct way to do it? | You can sum the series to get the charge, but not to get the potential. That sum does not converge. Instead, you need to think about the process you used to find the image charges and what that implies about the potential on the surface. |
| Feb 29 | I was wondering what sort of output is wanted? For a given set of parameters, should we list charges and other values? | Yes. Value and position of charges Potential at the three points on each sphere Total charge on each sphere Force between the spheres. |
| Feb 29 | When iterating, I was a little uncertain about what criteria
determines the total number of image charges. That is, when to stop
iterating.
Would this be determined by the number of charges in each sphere that
ensure points on the surface of the spheres are equipotentials or for which the ratio of the charges = Qa/Qb? |
Yes. No. |
| Feb 29 | Since the values of q(2) and other q(j)'s are based on the value of q(1), should qa(1) and qb(1) be assigned values, based on the ratio Qa/Qb? | Yes. You will then have the program adjust these values to get the right Qa/Qb when all the images are considered. |
| Feb 27 | For problem 2.6a, do you want us to re-derive the charge and location of an image charge inside a sphere due to a pt charge outside, or can we quote the results of the derivation from class and then explain why there must be infinitely many (which are image charges for the other image charges) inside each sphere? | You do not have to do a complete rederivation, but do discuss how the derivation will change as a result of the spheres not being grounded but instead each having a fixed charge. |
| Feb 15 | Do we need to find a general formula for C_ij in order to show the potential in the first part of problem 1.18a? | No |
| Feb 15 | Quick question for 1.17 part b. Is it safe to assume that the trial function we use is purely real? (no imaginary parts so no need for complex conjugates) | Yes |
| Feb 15 | in 1.18 a.) I want to know if arguing that all the charge is located on the surface 1 is enough to say that we can integrate over the surface instead of the volume and use sigma instead of rho? Or do you want it to be proved using a delta function where rho=(sigma_naught) * delta(x-x')? | One good sentence can take care of this. |