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Unformatted text preview: 58. (a) The magnitude of the toroidal ﬁeld is given by B0 = µ0 nip , where n is the number of turns per
unit length of toroid and ip is the current required to produce the ﬁeld (in the absence of the
ferromagnetic material). We use the average radius (ravg = 5.5cm) to calculate n:
ip = 400 turns
= 1.16 × 103 turns/m .
2π (5.5 × 10−2 m) B0
0.20 × 10−3 T
= 0.14 A .
−7 T · m/A)(1.16 × 103 /m)
(4π × 10 (b) If Φ is the magnetic ﬂux through the secondary coil, then the magnitude of the emf induced in that
coil is E = N (dΦ/dt) and the current in the secondary is is = E /R, where R is the resistance of the
The charge that passes through the secondary when the primary current is turned on is
q= is dt = N
R Φ dΦ =
R The magnetic ﬁeld through the secondary coil has magnitude B = B0 + BM = 801B0 , where BM
is the ﬁeld of the magnetic dipoles in the magnetic material. The total ﬁeld is perpendicular to the
plane of the secondary coil, so the magnetic ﬂux is Φ = AB , where A is the area of the Rowland
ring (the ﬁeld is inside the ring, not in the region between the ring and coil). If r is the radius of
the ring’s cross section, then A = πr2 . Thus
Φ = 801πr2 B0 .
The radius r is (6.0 cm − 5.0 cm)/2 = 0.50 cm and
Φ = 801π (0.50 × 10−2 m)2 (0.20 × 10−3 T) = 1.26 × 10−5 Wb .
q= 50(1.26 × 10−5 Wb)
= 7.9 × 10−5 C .
8.0 Ω ...
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