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Transcribed Image Text:shows a rectangular loop of wire immersed in
a nonuniform and varying magnetic field that is perpen-
dicular to and directed into the page. The field's magnitude
is given by B 4x², with B in teslas, r in seconds, and x
in meters. (Note that the function depends on both time
and position.) The loop has width W=3.0 m and height
H-2.0 m. What are the magnitude and direction of the
induced emf 8 around the loop at f= 0.10 s7
If the field varies with position,
we must integrate to get the
flux through the loop.
dA
B
B =
W
+
Figure 30-7 A closed conducting loop, of width W and height H,
lies in a nonuniform, varying magnetic field that points directly
into the page. To apply Faraday's law, we use the vertical strip of
height H, width dx, and area dA.
SM Figure 29-87 shows a cross section of
a hollow cylindrical conductor of radii a and
b, carrying a uniformly distributed current i.
(a) Show that the magnetic field magnitude
B(r) for the radial distance r in the range
b<r <a is given by
Hol
2x(a²-b²)
We start with a strip
so thin that we can
approximate the field as
being uniform within it.
2²-6²
r
(b) Show that when ra, this equation gives the magnetic field
magnitude B at the surface of a long straight wire carrying current i;
when r=b, it gives zero magnetic field; and when b= 0, it gives
the magnetic field inside a solid conductor of radius a carrying cur-
rent i. (c) Assume that a = 2.0 cm, b=1.8 cm, and i= 100 A, and
then plot B(r) for the range 0 <r<6 cm.
berca
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