2 TREATISE ON ALTERNATING CURRENTS. 



Such a curve is called a Line of Force, and the whole 

 space under the influence of the magnet is called its Field of 

 Force. 



2. Law Of Force. If two magnet poles of strengths m 

 and m' are situated at a distance r apart, they exert a mutual force 

 F t which is always given by the equation 



where k is a constant depending on the medium and the units 

 chosen. The force is attractive if m and m' have opposite signs, 

 and repulsive if they have like signs. The direction of the force 

 is in the straight line joining the poles. 



We choose our unit pole to be such that if two unit poles 

 are placed at a distance of one centimetre apart in air, the mutual 

 force exerted is equal to one dyne. The constant k then becomes 

 unity for air, and equation (1) takes the simpler form 



(2) 



If a magnetic field is due not to a single pole, but to any 

 distribution of poles, the force exerted upon a magnet pole placed 

 in it is still perfectly definite in magnitude and direction at 

 every point. The magnitude of the force exerted by a magnetic 

 field upon unit positive pole placed at any point is called the 

 Strength of the Field at that point, and the direction of 

 the field is taken to be that in which the unit positive pole is 

 urged. The direction of the field, then, is given at every point in 

 space by the line of force through that point. By a suitable con- 

 vention the strength of the field at every point can also be repre- 

 sented by means of lines of force. 



3. Convention for measuring Strength of 

 Field. The convention which is adopted in order to effect a 

 representation of the strength of a magnetic field is the assumption 

 of a uniform radiation of 4?rm lines of force from a pole of 

 strength m. 



Equation (2) shows that the force at a distance r from a pole 



of strength m is 5? 



If we suppose that such a pole is situated at the centre of 



