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



REFERENCES. 



On the general theory of the magnetic field produced by currents : 



MAXWELL. Electricity and Magnetism, Vol. n, Part iv, Chaps. I, n and xiv. 



J. J. THOMSON. Elements of the Mathematical Theory of Electricity and Magne- 

 tism, Chap. x. 



WINKELMANN. Handbuch der Physik (2te Auflage), Vol. i, p. 411. 

 HELMHOLTZ. Wissenschaftliche Abhandlungen, Band i. 



On galvanometers : 



MAXWELL. Electricity and Magnetism, Vol. n, Part iv, Chaps, xv and xvi. 



EXAMPLES. 



1. A current i flows in a very long straight wire. Find the forces and couples it 

 exerts upon a small magnet. 



Shew that if the centre of the small magnet is fixed at a distance c from the wire, it 

 has two free small oscillations about its position of equilibrium, of equal period 



where Mk 2 is the moment of inertia, and p the magnetic moment, of the magnet. 



2. Two parallel straight infinite wires convey equal currents of strength i in opposite 

 directions, their distance apart being 2. A magnetic particle of strength ju, and moment 

 of inertia mk 2 is free to turn about a pivot at its centre, distant c from each of the wires. 

 Shew that the time of a small oscillation is that of a pendulum of length I given by 



3. Two equal magnetic poles are observed to repel each other with a force of 40 dynes 

 when at a decimetre apart. A current is then sent through 100 metres of thin wire 

 wound into a circular ring eight decimetres in diameter and the force on one of the poles 

 placed at the centre is 25 dynes. Find the strength of the current in amperes. 



4. Regarding the earth as a uniformly and rigidly magnetised sphere of radius a, 

 and denoting the intensity of the magnetic field on the equator by H, shew that a wire 

 surrounding the earth along the parallel of south latitude X, and carrying a current i 

 from west to east, would experience a resultant force towards the south pole of the 

 heavens of amount 



5. Shew that at any point along a line of force, the vector potential due to a current 

 in a circle is inversely proportional to the distance between the centre of the circle and 

 the foot of the perpendicular from the point on to the plane of the circle. Hence trace 

 the lines of constant vector potential. 



6. A current i flows in a circuit in the shape of an ellipse of area A and length I. 

 Shew that the force at the centre is irilA. 



