IO2 



PROPERTIES OF CIRCULAR CURRENTS. 



744. If we apply this formula to the first term of the value of 

 X, that which represents the action of a circular current of radius r 

 on a point of the axis at the distance x, then denoting the mean 

 ruliivs by .7, a ad the radial and axial dimensions of the coil by 

 2C and 2^, we have 



p='4 



(4*2 - tf 



^6 



and the first term of the value X is equal to 



Fig. 138. 



745. For a point beyond the axis, if we stop at terms of the 

 second order in y, we may consider as constant the second value of 

 X in equation (33), which gives 



If we wish to push the approximation further, we shall apply 

 Maxwell's method to the correction, considering the term in y 2 as 

 constant. 



746. ACTION OF A COIL ON A MAGNETIC NEEDLE. In the 

 investigation of the galvanometer (particularly the tangent galvan- 

 ometer), we shall have to consider the action which the current of 

 a coil exerts on a magnetised needle. 



If the field of the coil were uniform, or the needle infinitely 

 small, the electromagnetic action would be reduced to a couple; 

 but in general it will be equal to a single force and to a couple. 



Let BB' (Fig. 138) be a circular current of radius a, the centre of 

 which is at O, Ox its axis, A 2 A x a needle the centre of which is on the 

 axis of the coil at a distance x from the centre. Let 2/ be the length 



