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

348 ANSWERS AND SOLUTIONS
cording to Lens's law, the total current in the coil decreases when the rod
enters it, and increases when the rod leaves it.
A diagram of the change in the current is shown in Fig. 463.
571. The magnetic flux changes at a constant rate, and therefore the e. m. f.
of induction in the second coil will also be constant. If the coil is connected
to a closed circuit, it will carry a direct current, which will set In not at
once, but depending on the coefficient of self..induction of the second coil and
its resistance.
572. Yes, it will. The e.m.f. of induction is proportional to the rate of
change of the magnetic flux, while the magnitude of the magnetic flux in
the iron core does not change directly with the current. The relationship will
be more complicated.
573. According to Faraday's law,
A«D
cCi= 10- S AT= 10- 8 kA
The e.m.f, of induction is numerically equal to the work performed by
the electric field when a single positive charge moves in the turn, i.e.,
cCi=2nrE. Hence E= 2 8 ; .
nr
Thus, we finally obtain:
E= 10_skn,r 2 =lO-skr
2nf 2
It should be noted that this electric field is induced not by the electric
charges, but by 8 magnetic field varying with time. Let us recall that when
an electric charge moves in a closed circuit in an electrostatic field the work
is always equal to zero. By an electrostatic field is meant an electric field
induced by electric charges.
574. Let us divide the ring into n=b 6 a small rings each with a width 6.
Let us consider a ring with a height h whose internal radius is x and external
radius is x+6. If 6 is small as compared with x, the resistance of such a
ring can be expressed by the formula
2nx
R=p?;ji
The e. m. f. of induction acting in this ring (if 6 ~ x) is equal to
L\(!)
8=10- 8 AT= 10-snx'k
The intensity of the current flowing in such a ring is
Al =