IÖ2 
THE QUANTUM 
[XII. 2 
2. A Quantum Magnetic Tube in Rotation 
We consider a single quantum tube such as would originate 
in a small magnet of magnetic moment M, and suppose it to be 
rotating with angular velocity co about the axis of the magnet. 
Let A be the area of cross-section, ds the length of an element of 
the tube at any point P (Fig. 24). 
The mass associated with each unit of volume of a magnetic 
Z 
Q 
R 
X 
Fig. 24.—Field due to a Small Magnet. 
field * is KB 2 /47r, where B = /¿H, consequently the mass of an 
KB 2 
element of the tube at P is -—-Ads. Draw a perpendicular PN 
from P to the axis of the magnet, and let the length of PN be />. 
Then the angular momentum of this element about the axis is 
KB 2 
-Ads x p 2 co. Now for a quantum tube the flux of magnetic 
induction, BA = /¿HA = h/e, and is constant along the tube. 
Therefore the angular momentum reduces to 
The angular momentum for the whole tube is found by 
integrating this expression throughout the length of the tube. 
* In this chapter the electric and magnetic co-efficients K and p will 
be retained in the analysis.