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Chapter 31
219
*P31.14
(a)
Each coil has a pulse of voltage tending to produce
counterclockwise current as the projectile
approaches, and then a pulse of clockwise voltage
as the projectile recedes.
(b)
v
d
t
==
×
=
−
150
10
625
3
.
m
2.40
s
ms
V
1
V
2
t
0
∆
V
FIG. P31.14
P31.15
εθ
θ
d
dt
NB
NB
t
A
A
2
2
cos
cos
ej
∆
∆
A
×
×−
×
°
=
−
−−
ε
∆
∆
t
cos
..
cos
.
.
80 0 10
0 400
50 600 10
200 10
30 0
136
3
66
V
s
T
T
m
af
a
f
a
f
Length
=
44
1
3
6
5
0
2
7
2
A
N
m
m
a
f
*P31.16
(a)
Suppose, first, that the central wire is long and straight. The enclosed current of unknown
amplitude creates a circular magnetic field around it, with the magnitude of the field given
by Ampere’s Law.
Bs
⋅=
z
dI
µ
0
:
B
It
R
=
µω
π
0
2
max
sin
at the location of the Rogowski coil, which we assume is centered on the wire. This field
passes perpendicularly through each turn of the toroid, producing flux
BA
0
2
IA t
R
max
sin
.
The toroid has 2
Rn
turns. As the magnetic field varies, the emf induced in it is
επ
ωµ
ω
=−
⋅ =−
N
d
dt
Rn
IA
R
d
dt
tI
n
A
t
2
2
0
0
max
max
sin
cos
.
This is an alternating voltage with amplitude
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Current

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