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Unformatted text preview: __—..___——__———___—__—.._—____—_——_——___—__—_—.._——_ 3. [6. Physics 1C Homework 3  Chapter 30: Inductance and Electromagnetic Oscillations (II) Determine the mutual inductance per unit length
between two long solenoids, one inside the other, whose radii are r1 and r2(r2 < r1) and whose turns per unit length
are £1 and}??? l gﬁﬁ‘ﬁ‘ﬁﬁﬁ‘ﬁi‘l‘i‘)‘ n n I r 2 lllll I]. I 'u' IIIIIII II ‘MMT’i’ (III) A long straight wire and a small rectangular wire 10,,
lie in the same plane, Fig. 30—14. Determine the mung
inductance in terms of 11 , 12, and w. Assume the wire is veri
long compared to [1, 12 and w, and that the rest of its drag
is very far away compared to 11 , [2 and w. I ~»«.
1 T
P w
I
t
i
i
12————>i FIGURE 30—14 Problem 5. (1.1) A toroid has a rectangular cross—section as shown in
Fig. 30—15. Show that the selfinductance is #0 N 2h
277' 72
1n—
’1 L Iﬁhere is the total number of turns and r1, r2, and h are the
dimensrons shown in Fig. 30—15. [Hint Use Ampére’s law to
get B as a function of r inside the toroid, and integrate] V" rr2 FIGURE 30—15 Problems 16 and 22.A toroid of 1'  . .
ectangular crosssectlon, With N turns carrying a
current I . , , 22h) (1) Determine the energy stored in the inductor L as a
function of time for the LR circuit of Fig. 30—5a. (2.) After how many time constants does the stored energy reach 7 99 percent of its maximum value? A B C “R
R L
IT
0.63 [max
Switch
V0 .
) 34‘. I (a (b) FIGURE 30—5 '(a) LR circuit;
(b) growth of current when
connected to battery. (11) A 760—pF capacitor is charged to 135V and then
quickly connected to a 175mH inductor. Determine (a) the frequency of oscillation, (b) the peak value of the current,
and (c) the maximum energy stored in the magnetic field of
the inductor. L l.
33% ~——l
‘ ‘ Switch
in . '5 who» 34 e 3 0 O
. (II) In the circuit of Fig. 30— , I .
each resistor (11, [2, 13) at the moment (a) the sw1tch 15 closed, (b) a long time after the switch is closed. After the
switch has been closed a long time, and reopened, what is
each current (c) just after it is opened, (d) after a long time? FIGURE 301 6
,, ,EKOPEHQQ; Bonus Problems 48%,) Show that the selfinductance L of a toroid (Fig. 30—18)
* of radius r0 containing N loops each of diameter d is
“0 de2 8’0 if ,0 >> d. Assume the field is uniform inside the toroid' is
this actually true? Is this result consistent with L for a sole—
noid? Should it be? (b) Calculate the inductance L of a
large toroid if the diameter of the coils is 2.0 cm and the diameter of the whole ring is 50 cm. Assume the field
inside the tor01d is uniform. There are a total of 550 100 s
of wire. p Lz Path 1 FIGURE 30:1 A toroidr, Problem 48. 46. Estimate the mutual inductance M between two small 100 of radius r1 and r2, which are separated by a distance 1 £11?
is large compared to r, and r2, Fig. 30—17. Give M as:
function of 0, the angle between the planes of the two coilgg
Assume the line joining their centers is perpendicular mild: plane of coil 1. FIGURE 30—17 Problem 46. ...
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