78 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



is just what it is, even though it lies in the radiofrequency range and for 

 technical reasons appears on a scope instead of on a photographic film. 



The peak is the phenomenon of magnetic resonance. We shall now 

 interpret it in terms of theory somewhat oversimplified, for it is not the 

 office of these opening paragraphs to introduce all of the complexities 

 of quantum mechanics. 



In Fig. 1, inside the rectangle which represents the sample, appear a 

 number of arrows. These are symbols of the protons. In other circum- 

 stances we might imagine the protons as solid balls, in still others we 

 might imagine them as centres of force; but for the present purpose we 

 are regarding them as tiny bar-magnets, and the arrows symbolize the 

 directions in which they are pointing. It is necessary to label these 

 directions with perfect clearness. The figure has been drawn with the 

 south pole-piece of the big magnet (the one responsible for the big field 

 H) above. The point of each arrow represents the north pole of the 

 protonic magnet. 



Thus the arrows pointing upward represent protons in the orientation 

 into which the big field would like to turn the protonic magnets, and 

 would indeed succeed in turning them if they were literal compass- 

 needles in literal compasses. The arrows pointing downward represent 

 protons in the opposite orientation. I will call these, for shortness, the 

 "up" orientation and the "down" orientation. Evidently if the physicist 

 could reach into the sample with fingers or with forceps and turn a 

 proton from the up orientation into the down one, he would be doing 

 work upon the proton at the expense of energy from his muscles. Well, 

 he cannot reach into the sample with fingers or with forceps and grasp 

 and turn a proton. But he can reach into the sample with the oscillating 

 field and turn the protons, and this is the experiment we are considering. 

 Magnetic resonance is the turning of protons from the up orientation 

 into the down one, from the orientation or ''level" of lesser energy into 

 the orientation or level of greater energy. 



But why does the effect occur at one frequency only? And what 

 determines that frequency? To cope with this problem we shall have to 

 introduce symbols, equations, and quantitative reasoning. 



The first step is to evaluate the work required to turn the proton, or, 

 in other words, the energy-difference between the two orientations or 

 levels. It shall be denoted by Wy and the magnetic moment of the 

 proton by /Xp . We proceed by strictly classical reasoning. The torque 

 exerted on the proton by the magnetic field H is -fipH sin 0. Here 6 stands 

 for the angle between the direction of the steady field and the direction 

 in which the magnetic moment of the proton is pointing. We have 



