From key@physics.utoronto.ca Fri Apr 11 11:34:25 2008
Date: Fri, 11 Apr 2008 11:34:23 -0400
From: Tony Key <key@physics.utoronto.ca>
To: hanfei.luo@utoronto.ca
Subject: Re: PHY138 Problems

Hi Hank - thanks for your kind words.  I, too, have enjoyed our email chats!

Sorry if my language was confusing.  N(a), as you can see from its
definition, is the number 'up' (n+) MINUS the number 'down' (n-). the ratio
of up to down is exp(- delta_E/kT).  So indeed it is a math problem from now
on.  The magnetization is then given by mu*N(a).  Also remember that N_T is
equal to  n+ PLUS n-.  Make an equation for the quotient of M (the required
variable) and N_T in terms of mu and n+ and n_.  Divide numerator and
denominator by n- .  Put in the value for n+/n- - exp(  ).  Approximate
exp(x) by 1 + x ; then neglect x compared to 2.

Let me know if that works.

Sorry about the faradays law one.  1. It's hard to get decent problems,
given the basic nature of my presentation on MRI, so I was glad to find one
in Knight; 2. I had mentioned Faraday's Law in an early class (it's needed
to explain Maxwell's result); 3. Knight's question is dead simple; 4.I
thought it might be good for your soul to at least have to do a little
research and learn about Faraday's law, which is also the basis of all power
generation.  5. A little revision of magnetic field and magnetic flux won't
do any harm!

I think KNight's presentation is quite good.  Faraday's law says that a
changing magnetic field produces an electric field (there is another law
that says a changing electric field produces a magnetic field - that's the
one that makes the  spinning proton have its magnetic field). The
relationship is that a rate of change of magnetic flux through a given area
is equal to the electromotive force (the emf) round the periphery of the
area.  Magnetic flux is just the product of the magnetic field and the area
it passes through.  All a bit mysterious, but that's god for you!

Hope that helps.

Have a good summer,

TonyK

hanfei.luo@utoronto.ca wrote:
> Dr. Key:
>   It's Hank again. Thanks for your fair test, it was much appreciated 
> (and I will miss you :D), but now I really want to talk about macroscopic
> magnetic moment. The problem is this week's MP's first problem.
>   According to you, to quote, "N(a) is defined here as the number of 
> protons aligned with the magnetic field minus the number aligned against
> the field - i.e. the excess of the 'up' protons over the 'down' protons.".
> The first half of this sentence says N(a) as a difference between two
> numbers (since you said "minus") and the second part says N(a) as a ratio
> between two numbers (since you said "over"). What's going on??? And this
> also left me confused about which proton is of the higher energy
> level----up proton or low proton?
>   Then, suppose I know the ratio of # of higher-energy protons over 
> the # of lower-energy protons and I know the sum of higher-energy photon #
> and lower-energy photon #, how do I figure out the difference between
> these two values? It's more of a math problem: given the ratio of two
> values and the sum of two values, how do we figure out the difference (or
> given the the ratio and difference, how do we figure out the sum)? I am
> sorry that I am not good at math.
>   By the way, I might ask well ask you one more question about that 
> Faraday's law question (I will never curse you, by the way :D). I got it
> right, but it was kind of blindly plugging the formula. From what I
> understood that Faraday's law require the cross-section area to be a
> circle (since it has something to do with loops), but a patient's
> cross-section is not a circle. So what's going on here? Can you just teach
> me in details about Faraday's law?
>   Thanks! I hope this letter is not too long, but questions are 
> questions..
>
> Hank
>