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θ
=
π
/2 position (where its midpoint will reach a distance of
a
above the plane of the
figure). At the moment it is in the
=
π
/2 position, the area enclosed by the “circuit” will
appear to us (as we look down at the figure) to that of a simple rectangle (call this area
A
0
which is the area it will again appear to enclose when the wire is in the
= 3
π
/2 position).
Since the area of the semicircle is
π
a
2
/2 then the area (as it appears to us) enclosed by the
circuit, as a function of our angle
, is
AA
a
=+
0
2
2
π
cos
where (since
is increasing at a steady rate) the angle depends linearly on time, which
we can write either as
=
ω
t
or
= 2
π
ft
if we take
t
= 0 to be a moment when the arc is
in the
= 0 position. Since
G
B
is uniform (in space) and constant (in time), Faraday’s law
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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