Effect of a Changing Magnetic Field. 463 



wot be sufficient to prevent all motion. More important than 

 this friction is the directive moment due to the mutual elec- 

 trostatic attraction of the condenser plates. It is mechani- 

 cally impossible to construct plates so absolutely symmetrical 

 that the directive force due to a non-homogeneous electro- 

 static field is not very many times as great as that of a 

 delicate suspension fibre such as Cremieu used, and on the 

 basis of whose moment of torsion alone the expected deflexion 

 is calculated. The apparently negative result would there- 

 fore be unconvincing, even if, according to theory, a deflexion 

 -should take place. But this is not the case. A simple 

 calculation* will show that the magnetic effect on the 

 charging current, which passes down the suspended frame, 

 through the magnetic field while at its maximum value, each 

 time the charge on the plates is reversed, will produce a 



* Let the charging current dQ/dt pass along an elementary arc dl 

 whose radius is r measured from the '• pole " of the magnet as centre, 

 and the plane of the arc passing through the axis of the magnet. The 

 force perpendicular to the plane of the arc will be : 



dF= il ^.dl.K 



dt 



dQ m 



= df' dl 'r<> 



where H is the intensity of the magnetic field, and m is the strength of 

 the pole. 



The elementary moment around the axis of the magnet is then : 



dL = ~yf .dl . — sin d 

 dt r ' 



= ~ . m sin $ dQ, 

 at 



where Q is the angle between r and the axis of the magnet. Now since 

 the average value of'dQ/dt is '2nQ, where n is the number of reversals of 

 the charge per second, and since m = N/47r, where N is the total magnetic 

 flux frompole to pole, we have : 



dL= n 9>~smddd, 

 2n 



which is seen to be independent of r. 



The total moment exerted on a conductor carrying a current of average 

 value 2nQ from a point on the axis beyond the pole to a point on the 

 middle of the magnet will be, regardless of the path, 



mQN C" 



sm dQ = -^— 



Jo 



ide 

 the 

 of. the two moments are opposite is easily seen bv applving the familiar 

 motor " and " dynamo " rules. 



which is the same in magnitude as the moment exerted on the charge 

 Q by n reversals per second of the magnetic flux N. That the directions 



