422 The Magnetic Field produced by Electric Currents [CH. xm 



It follows that the force outside the solenoid can have no component at 

 right angles to planes through the axis, and clearly, by a similar argument, 

 the same must be true inside the solenoid. Hence the lines of induction 

 must lie entirely in the planes through the axis of the 

 solenoid. From symmetry, there is no reason why 

 the lines of induction at any point should converge 

 towards, rather than diverge from, the axis, or vice 

 versa. Hence the lines of induction will be parallel 

 to the axis, and the force at every point will be entirely 

 parallel to the axis. 



Let the lines PQR, P'Q'R in fig. 128 be radii 

 meeting the axis, the lines PP', QQ', RR' being 

 parallel to the axis and each of length e. Let the FIG. 128. 



magnetic forces along these lines be F lf F 2 and F 3 

 respectively. 



In taking unit pole round the closed path PP'Q'QP the work done is 



F l e-%e, 



and since this must vanish, we must have F = F 2 . Hence the force at all 

 points outside the solenoid must be the same ; it must be the same as the 

 force at infinity and must consequently vanish. Thus there is no force at all 

 outside the solenoid. 



In taking unit pole round the closed path PP'R'RP, the work done is 

 F 3 e, and this must be equal to 47rm'e, so that we must have F 3 = 4nrni. Thus 

 the force at any point inside the solenoid is a force 4>7rni parallel to the axis. 



Thus the field of force arising from an infinite solenoid consists of a 

 uniform field of strength ^irni inside the solenoid, there being no field at all 

 outside. The construction of a solenoid accordingly supplies a simple way of 

 obtaining a uniform magnetic field of any required strength. 



GALVANOMETERS. 



492. A galvanometer is an instrument for measuring the strength of 

 an electric current, the method of measurement usually being to observe the 

 strength of the magnetic field produced by the current by noting its action 

 on a small movable magnet. 



There are naturally various classes and types of galvanometers designed 

 to fulfil various special purposes. 



The Tangent Galvanometer. 



493. In the tangent galvanometer the current flows in a vertical 

 circular coil, at the centre of which a small magnetic needle is pivoted 

 so as to be free to turn in a horizontal plane. 



