of the ring and increased with time according to a certain law B (t).
Find the angular velocity co of the ring as a function of the induction
B (t).
3.312. A thin wire ring of radius a and resistance r is located in-
side a long solenoid so that their axes coincide. The length of the
solenoid is equal to 1, its cross-sectional radius, to b. At a certain
moment the solenoid was connected to a source of a constant voltage
V. The total resistance of the circuit is equal to R. Assuming the
inductance of the ring to be negligible, find the maximum value of
the radial force acting per unit length of the ring.
3.313. A magnetic flux through a stationary loop with a resistance
R varies during the time interval i as (120 = at (r — t). Find the
amount of heat generated in the loop during that time. The inductance
of the loop is to be neglected.
3.314. In the middle of a long solenoid there is a coaxial ring of
square cross-section, made of conducting material with resistivity
p. The thickness of the ring is equal to h, its inside and outside radii
are equal to a and b respectively. Find the current induced in the
ring if the magnetic induction produced by the solenoid varies withtime as B = pt, where 3 is a constant. The inductance of the ring
is to be neglected.
3.315. How many metres of a thin wire are required to manufac-
ture a solenoid of length / 0 = 100 cm and inductance L = 1.0 mH
if the solenoid's cross-sectional diameter is considerably less than its
length?
3.316. Find the inductance of a solenoid of length 1 whose
winding is made of copper wire of mass m. The winding resistance
is equal to R. The solenoid diameter is considerably less than its
length.
3.317. A coil of inductance L = 300 mH and resistance R =
= 140 m52 is connected to a constant voltage source. How soon will
the coil current reach ri = 50% of the steady-state value?
3.318. Calculate the time constant ti of a straight solenoid of length
/ = 1.0 m having a single-layer winding of copper wire whose total
mass is equal to m = 1.0 kg. The cross-sectional diameter of the
solenoid is assumed to be considerably less than its length.
Note. The time constant ti is the ratio LIR, where L is inductance
and R is active resistance.
3.319. Find the inductance of a unit length of a cable consisting
of two thin-walled coaxial metallic cylinders if the radius of the out-
side cylinder is = 3.6 times that of the inside one. The perme-
ability of a medium between the cylinders is assumed to be equal to
unity.
3.320. Calculate the inductance of a doughnut solenoid whose
inside radius is equal to b and cross-section has the form of a square
with side a. The solenoid winding consists of N turns. The space in-
side the solenoid is filled up with uniform paramagnetic having per-
meability p.
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