Irodov – Problems in General Physics

L2

in the same plane, with the side b being closest to the wire, separated
by a distance^1 from it and oriented parallel to it.

L7

Fig. 3.93. Fig. 3.94.

3.330. Determine the mutual inductance of a doughnut coil and

an infinite straight wire passing along its axis. The coil has a rectan-

gular cross-section, its inside radius is equal to a and the outside one,

to b. The length of the doughnut's cross-sectional side parallel to the

wire is equal to h. The coil has N turns. The system is located in a

uniform magnetic with permeability IA.

3.331. Two thin concentric wires shaped as circles with radii a

and b lie in the same plane. Allowing for a < b, find:

(a) their mutual inductance;

(b) the magnetic flux through the surface enclosed by the outside

wire, when the inside wire carries a current I.

3.332. A small cylindrical magnet M (Fig. 3.95) is placed in the

centre of a thin coil of radius a consisting of N turns. The coil is con-

nected to a ballistic galvanometer. The active resistance of the whole

circuit is equal to R. Find the magnetic moment of the magnet if

its removal from the coil results in a charge q flowing through the

galvanometer.

3.333. Find the approximate formula expressing the mutual in-

ductance of two thin coaxial loops of the same radius a if their cen-

tres are separated by a distance 1, with 1> a.

L,R

Fig. 3.95.

3.334. There are two stationary loops with mutual inductance

La. The current in one of the loops starts to be varied as / 1 = at,

where a is a constant, t is time. Find the time dependence / 2 (t) of

the current in the other loop whose inductance is L2 and resistance R.

3.335. A coil of inductance L = 2.0 μH and resistance R = 1.0 S2

is connected to a source of constant emf g = 3.0 V (Fig. 3.96). A