6.007  Electro Energy Motors to Laser

Spring 2008 : Problem 5c (page 32 in the packet) The solutions are using a horrible choice of variables in their expression for Beers Law! Instead of alpha (which we used in lecture 17) they are using kappa which is what we have been using for the imaginary part of the refractive index. Also, they were really sloppy about writing kappa and it looks like a k in the answer blank.

Spring 2009 : Problem 1g (page 41 in the packet) The wavelength given for the electron is wrong (by a factor of 10). It should be 0.12angstroms. The short version of why is Energy=h*f and lambda = h/momentum (momentum = sqrt(2 * m * KE) for a non relativistic particle) are both valid, but the phase velocity relating the two is NOT the speed of light and is NOT the velocity of the particle. If you calculate the wavelength using lambda=h/sqrt(2m_e*KE) you'll get the right result, so do that if it comes up on the final.

Fall 2012  : Problem 2d  (page 78 in the packet) To make it clear that the force changes signs they've pulled out a negative sign. But to do that they should have wrote |mu-mu_o| instead of (mu-mu_o).

The sqrt(2) in the solution should be a 2 for peak intensity or a 1 for time average intensity. The amplitude of E is not E_o, it is E_o*sqrt(2) because the polarization vector (x_hat - z_hat) does not have a magnitude of 1. The solutions are assuming peak intensity and forgot to square the sqrt(2) when computing |E|^2.

-Bill

Hi Everyone,

In the quiz two solution for the stacked dielectric I think there's an error in the setup of the solution, but the end result is correct.

The result should be that the phase difference between the two paths (path A: reflect from first surface, path B: travel through the layer, reflect from second surface, and then travel back to the first surface) is a multiple of 2pi to get maximum reflection from the stack.

Because the material is stacked n_lo - n_hi - n_lo - n_hi - ... there is a phase change of pi on reflection from one of the two interfaces (lo to hi or hi to low, I'll let you figure it out). Depending on if you look at a n_lo - n_hi - n_lo stack or a n_hi - n_lo - n_hi stack you'll either see the phase change on reflection in path A or path B.

The end result is correct: each layer should be lambda_o / (4*n_layer) thick for maximum reflection. You should prove this to yourselves.

This looks like it conflicts with the zero reflection three-layer system we looked at in lecture 22 but it does not. (A new version of the lecture 22 pdf has been posted, there were some boxes where symbols should have been in the old version). That result required (1) for you to choose a specific n2, and (2) that the system be exactly one thin layer between two infinitely thick layers. If you draw out the first six or seven layers of the quiz two system you'll see that even if you pick the first dielectric exactly wrong there will still be reflections due to dielectric layers 3+ .

-Bill

Also: you can see old announcements on the front page of the class stellar site by clicking the link 'see archived announcements' at the bottom of the page.

Hi,

Spring 2009, problem 6, uses |T|^2 as the tunneling probability, when it should be using T. See lecture 32 for more information (the approximate solution is given on page 7 of the lecture notes).

Something also worth looking at: Spring 2008 problem 3c. The solutions model the magnet as a battery, but in lecture I told you to model a magnet as a current source. A permanent magnet does not behave exactly like a current source or exactly like a voltage source in the magnetic circuits model. If you have no other sources of flux in the system, you can do a good job modeling the magnet as a current source (it will produce the same flux regardless of the reluctance it's attached to). However, if you set up a coil and drive the coil you can change the flux through the magnet. For 99% of what we're using the model for, it's perfectly fine to model it as a current source. If you're asked to model a magnet in a magnetic circuits problem, pick a model and explain why you're using it.

-Bill

For the final exam you will be allowed two sheets of notes instead of the single sheet allowed during the midterms. The final exam will cover material from the entire semester (just like the example finals posted online), so make sure you study everything we've covered this term.

-Bill