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

120 PROBLEMS
is , and its length l (r ~ I). The resistance of the wire is R.
What should the voltage at the ends of the solenoid be for the
current flowing in it to increase directly with time, i.e., I =kt?
587. A solenoid (see Problem 586) is connected to a battery
whose e.m.I. is cC. The key is closed at the moment t = O. What
is the intensity of the current flowing through the circuit of
the solenoid if the resistance R of the solenoid, battery and
feeding wires is neglected?
588. Calculate the work of the battery (see Problem 587)
during the time 1". What kind of energy is this work converted
into?
589. A ring made of a superconductor is placed· into a homogeneous
magnetic field whose intensity grows from zero to H o •
The plane of the ring is perpendicular to the force lines of the
field. Find the intensity of the induction current appearing in
the ring. The radius of the ring is , and its inductance L.
590. A superconductive ring with a radius r is in.a homogeneous
magnetic field with an intensity H~ The force lines of the
field are perpendicular to the plane of the ring. There is no
current in the ring.
Find the magnetic flux piercing the ring after the magnetic
field is swi tched off.
591. Find the inductance of a coil wound onto the iron core
shown in Fig. 211. The number of turns of the coil N, the
cross-sectional area A, the perimeter of the core (medium line)
I and the permeability of the core l-t, are known.
Note. Take into account the fact that .the intensity of the
magnetic field inside the core is practically constant and can
be approximately expressed by the formula H = OAn ~ I.
592. Estimate approximately the coefficient of mutual inductance
of the windings of a transformer. Consider the windings
Fig. 211 Fig. 212