Shielding of Concentric Spherical Shells. 



103 



a /a v 



*/*o- 



0-9 

 0-8 

 0-7 

 06 

 05 



1/60 



1/108 



1/146 



1/174 



1/194 



This table illustrates the difficulty of improving the 

 shielding by increasing the thickness of a shield already 

 moderately thick. When the latter is increased in the ratio 

 5 : 1, and the internal empty space is reduced sixfold, the 

 shielded field is only reduced in the ratio of about 1 : 3. 



In general, if the volume of the material employed in a 

 shell is seven times that of the internal spherical space the 

 external field will be reduced to 1/100, 1/200, or 1/300 of 

 its unshielded value, according as the permeability of the 

 material is 500, 1000, or 1500. 



'Next consider the case of a small magnet placed at a 

 distance b from the centre of the shell. 



If the axis of the magnet lies on a diameter, and if the 

 moment is ^ , the unshielded potential is 



JP,2P 2 & 3P 3 6 2 



+o{i> + 



+ 



+ &C 



nVM 1 ' 1 



v n+i 



+ &c 



•}■ 



where r is measured from the centre of the sphere. 



To find the potential in the shielded field, we must multiply 

 each term in the expression by the corresponding value of 



«o^(N + l) 2 



Q$ f i 1 +l)^ + fjL 1 )« -.N« 1 ( fJ L 1 -iy> 



which may be called the shielding factor. 



If the shell is thin, so that a =«! — £, where t is small, this 

 factor (remembering that a = a-( 2w+1 )) becomes 



fli 2n+ Vi(N + l) a 



a 1 2w + 1 /*i(N + l) 2 +(2« + l)N(/A 1 -l) 2 a 1 ^ 



(2*1+1)/*! 



(2%+1K+w(« + 1)(/ai-1)^M 5 



which, if fjbi is large, simplifies to 



2?2 + l 



2n + 1 + n (n + l)/A 1 £/a l " 



