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71. (a) We assume the current is changing at (nonzero) rate
di/dt
and calculate the total emf across both
coils. First consider the coil 1. The magnetic ±eld due to the current in that coil points to the right.
The magnetic ±eld due to the current in coil 2 also points to the right. When the current increases,
both ±elds increase and both changes in ﬂux contribute emf’s in the same direction. Thus, the
induced emf’s are
E
1
=
−
(
L
1
+
M
)
di
dt
and
E
2
=
−
(
L
2
+
M
)
di
dt
.
Therefore, the total emf across both coils is
E
=
E
1
+
E
2
=
−
(
L
1
+
L
2
+2
M
)
di
dt
which is exactly the emf that would be produced if the coils were replaced by a single coil with
inductance
L
eq
=
L
1
+
L
2
+2
M
.
(b) We imagine reversing the leads of coil 2 so the current enters at the back of coil rather than the
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 Fall '08
 SPRUNGER
 Physics, Current

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