180 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 3 



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3-11. Induction Systems, Search Coils 



A coil having n turns and an average area a is placed in a magnetic 

 field of uniform strength H, Fig. (3-1)1. The direction of the mag- 

 netic field is perpendicular to the plane formed by the loop. Any 

 change of the magnetic field produces an instantaneous voltage e c 



between the loop terminals, which is propor- 

 tional to the rate of change of the magnetic 



field 



dH 

 e = napi —— (la) 



where // is the magnetic permeability. If the 

 direction of the magnetic field is not parallel 

 to the coil axis but forms an angle <x with the 

 axis, Eq. (la) changes to 



H,B 



Fig. (3-1)1. Search-coil 

 magnetic transducer. 



na/ii 



dH 



lit 



cos a 



(2) 



The magnetic field strength H corresponds to a magnetic flux 

 density of magnitude 



B = piH (3) 



so that Eq. (la) can be written as 



dB 



na 



dt 



The total flux through the area a of the loop is defined as 



O = ajuH = aB 

 so that Eq. (la) can also be written as 



d0> 



e °= n Tt 



(lb) 



(4) 



(lc) 



The Eqs. (la), (16), and (lc) describe the relationship between the 

 rate of change of a magnetic flux through a loop and the voltage 

 induced in the loop. In general, however, the input magnitudes to 

 be converted into electrical signals are not the time derivatives of 

 H, B, or O but the magnitudes themselves. The integral form of 

 Eq. (la) furnishes a relationship between any change of the magnetic 

 field AH and the transducer output. 



e dt = na/j, AH 



(5a) 



That is, the voltage-time integral appearing at the transducer output 

 is proportional to the change of the magnetic field strength AH 



