Bukhovtsev-et-al-Problems-in-Elementary-Physics

ELECTRICITY AND MAGNETISM
353
Fig. 466
The work of the force F over the path S is spent to increase the kinetic
energy of the conductor and the electrostatic energy of the capacitor.
585. Let the magnet be initially positioned as shown in Fig. 466. Its
north end is at a distance R1 from the current and its south end at a distance
R2' the length of the magnet being 1= R2 - R1. Let us now move the
magnet in the plane ~ around the wire, keeping the distances R 1 and R t
unchanged until after one revolution the magnet occupies its initial position.
Since during this motion the total change in the magnetic flux through the
area restricted by the straight wire and the conductors that short-circuit the
current at a great distance from the magnet is zero, the quantity of induced
electricity that has flown through the circuit is also zero. On the basis of
the law of conservation of energy, the work of the forces of the magnetic
field should also be equal to zero:
2n R 1 H t m- 2n R 2 H 2 m= O
where m is the magnetic charge of the pole, and HI and H2 are the intensities
of the magnetic field at the distances R1 and R t from the wire.
Hence, Z:=~: which is possible only when H is proportional to ~ .
586. Since according to the initial condition, the intensity. of the magnetic
field is directly proportional to time, i. e., H =0.4 n 7kt, then the e. m. 1.
of self-induction is equal to
N2